32581 + Interview Questions in Mathematics Page 19 InterviewSolution

901.	Two triangles are said to be similar, if the corresponding sides are___ and the corresponding angles are___.
Answer» Two triangles are said to be similar, if the corresponding sides are___ and the corresponding angles are___.

Discussion

902.	Question 3 (iii)The points A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of Δ ABC.Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ:QE = 2:1 and CR:RF = 2:1.
Answer» Question 3 (iii) The points $A (x_{1}, y_{1}), B (x_{2}, y_{2}) a n d C (x_{3}, y_{3})$ are the vertices of $Δ$ ABC. Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ:QE = 2:1 and CR:RF = 2:1.

Discussion

903.	Rationalise the denominator and simplify(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)
Answer» Rationalise the denominator and simplify (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

903.

Rationalise the denominator and simplify(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

Answer»

Rationalise the denominator and simplify

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

Discussion

904.	If the difference of mode and median of a data is 24, then the difference of median and mean is(a) 12(b) 24(c) 8(d) 36
Answer» If the difference of mode and median of a data is 24, then the difference of median and mean is (a) 12 (b) 24 (c) 8 (d) 36

Discussion

905.	Question 5A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60∘. Find the length of the string, assuming that there is no slack in the string.
Answer» Question 5 A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is $60^{\circ}$ . Find the length of the string, assuming that there is no slack in the string.

Discussion

906.	The value of (1 - Cos A)(1 + Cos A)(cosec2A) is __
Answer» The value of (1 - Cos A)(1 + Cos A)( $c o s e c^{2}$ A) is __

Discussion

907.	The shadow of a tower, when the angle of elevation of the sun is 45°, is found to be 10 m longer than when it was 60°. Find the height of the tower.
Answer» The shadow of a tower, when the angle of elevation of the sun is 45°, is found to be 10 m longer than when it was 60°. Find the height of the tower.

Discussion

908.	Find the H.C.F. of (3m3−12m2+21m−18) and (6m3−30m2+60m−48) by using the division method.
Answer» Find the H.C.F. of $(3 m^{3} - 12 m^{2} + 21 m - 18)$ and $(6 m^{3} - 30 m^{2} + 60 m - 48)$ by using the division method.

Discussion

909.	If p(x)=x−x2−2,then find p(1).
Answer» $If p (x) = x - x^{2} - 2, then find p (1) .$

Discussion

910.	The length of the diagonal of a square is 102cm. Its area is(a) 200 cm2(b) 100 cm2(c) 150 cm2(d) 1002 cm2
Answer» The length of the diagonal of a square is $10 \sqrt{2} cm .$ Its area is (a) 200 cm² (b) 100 cm² (c) 150 cm² (d) 100 $\sqrt{2}$ cm²

Discussion

911.	Fill in the blanks using the correct word given in brackets :(i) All circles are ......... (congruent, similar).(ii) All squares are ........(similar, congruent).(iii) All .......... triangles are similar (isosceles, equilateral):(iv) Two triangles are similar, if their corresponding angles are .......... (proportional, equal)(v) Two triangles are similar, if their corresponding sides are ........... (proportional, equal)(vi) Two polygons of the same number of sides are similar, if (a) their corresponding angles are and (b) their corresponding sides are ...........(equal, proportional).
Answer» Fill in the blanks using the correct word given in brackets : (i) All circles are ......... (congruent, similar). (ii) All squares are ........(similar, congruent). (iii) All .......... triangles are similar (isosceles, equilateral): (iv) Two triangles are similar, if their corresponding angles are .......... (proportional, equal) (v) Two triangles are similar, if their corresponding sides are ........... (proportional, equal) (vi) Two polygons of the same number of sides are similar, if (a) their corresponding angles are and (b) their corresponding sides are ...........(equal, proportional).

Discussion

912.	Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that APAB=35. [CBSE 2011]
Answer» Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that $\frac{AP}{AB} = \frac{3}{5}$ . [CBSE 2011]

Discussion

913.	Question 97How many cubes each of side 0.5 cm are required to build a cube of volume of 8 cm3?
Answer» Question 97 How many cubes each of side 0.5 cm are required to build a cube of volume of $8 c m^{3}$ ?

913.

Question 97How many cubes each of side 0.5 cm are required to build a cube of volume of 8 cm3?

Answer»

Question 97

How many cubes each of side 0.5 cm are required to build a cube of volume of $8 c m^{3}$ ?

Discussion

914.	In figure, Point G is the point of concurrence of the medians of △PQR. If GT = 2.5, find the lengths of PG and PT.
Answer» In figure, Point G is the point of concurrence of the medians of $△$ PQR. If GT = 2.5, find the lengths of PG and PT.

Discussion

915.	Two cubes have their volumes in the ratio 1 : 27. What is the ratio of their surface areas?
Answer» Two cubes have their volumes in the ratio 1 : 27. What is the ratio of their surface areas?

Discussion

916.	in triangle PQR right angled at Q, PQ=QR, if QS is perpendicular to PR and QS=4cm, then the perimeter of triangle PQR is
Answer» in triangle PQR right angled at Q, PQ=QR, if QS is perpendicular to PR and QS=4cm, then the perimeter of triangle PQR is

Discussion

917.	AB is a diameter of a circle and AC is its chord such that ∠BAC = 30°. If the tangent at C intersects AB extended at D, then BC = ________.
Answer» AB is a diameter of a circle and AC is its chord such that ∠BAC = 30°. If the tangent at C intersects AB extended at D, then BC = ________.

Discussion

918.	If arc ABC=130∘ and arc CDE=110∘, then the measure of arc ACE is equal to?
Answer» If $a r c A B C = 130^{\circ}$ and $a r c C D E = 110^{\circ},$ then the measure of arc ACE is equal to?

Discussion

919.	Solve the following quadratic equations by factorization:abx2+b2-acx-bc=0
Answer» Solve the following quadratic equations by factorization: $a b x^{2} + (b^{2} - a c) x - b c = 0$

Discussion

920.	The sides of a right angled triangle are 5x, 4x and 3x units respectively. If the perimeter is 36 units, what is x? ___
Answer» The sides of a right angled triangle are 5x, 4x and 3x units respectively. If the perimeter is 36 units, what is x? ___

Discussion

921.	A company manufactures cassettes. Its cost and revenue functions are C(x) = 26,000 + 30x and R(x) = 43x, respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realize some profit?
Answer» A company manufactures cassettes. Its cost and revenue functions are C(x) = 26,000 + 30x and R(x) = 43x, respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realize some profit?

Discussion

922.	Determine the ratio in which the straight line x - y- 2 = 0 divides the line segment joining (3, -1) and (8, 9).
Answer» Determine the ratio in which the straight line x - y- 2 = 0 divides the line segment joining (3, -1) and (8, 9).

Discussion

923.

The following distribution gives daily income of 50 workers of a factory: Daily income(in ₹): 200 – 220 220 – 240 240 – 260 260 – 280 280 – 300 Number of workers: 12 14 8 6 10 Convert the distribution above to a 'less than type' cumulative frequency distribution and draw its ogive.

Answer» The following distribution gives daily income of 50 workers of a factory:

Daily income(in ₹):	200 – 220	220 – 240	240 – 260	260 – 280	280 – 300
Number of workers:	12	14	8	6	10

Convert the distribution above to a 'less than type' cumulative frequency distribution and draw its ogive.

Discussion

924.	An object is thrown at an angle 'θ' with horizontal. If elevation angle of the object at its highest point as seen from the point ofprojection is †an^{-1}(1/2), then θ is equal to (1) 30^° (2) 45^° (3) 60^° (4) 37^°
Answer» An object is thrown at an angle 'θ' with horizontal. If elevation angle of the object at its highest point as seen from the point ofprojection is †an^{-1}(1/2), then θ is equal to (1) 30^° (2) 45^° (3) 60^° (4) 37^°

Discussion

925.	(cosA−sinA+1)(cosA+sinA−1)= _________.
Answer» $\frac{(c o s A - s i n A + 1)}{(c o s A + s i n A - 1)} =$ _________.

Discussion

926.	Solve for x: √x2+x−6−x+2=√x2−7x+10,xϵR
Answer» Solve for x: $\sqrt{x^{2} + x - 6} - x + 2 = \sqrt{x^{2} - 7 x + 10}, x ϵ R$

926.

Solve for x: √x2+x−6−x+2=√x2−7x+10,xϵR

Answer»

Solve for x:

$\sqrt{x^{2} + x - 6} - x + 2 = \sqrt{x^{2} - 7 x + 10}, x ϵ R$

Discussion

927.	A solid cone of base radius 10 cm is cut into two parts through the midpoint of its height, by a plane parallel to its base. Find the ratio of the volumes of the two parts of the cone.
Answer» A solid cone of base radius 10 cm is cut into two parts through the midpoint of its height, by a plane parallel to its base. Find the ratio of the volumes of the two parts of the cone.

Discussion

928.	If the speed of the boat in still water is xkmh and speed of the stream is ykmh . S1 : upstream speed of the boat is (x−y)kmh S2 : downstream speed of the boat is (x+y)kmh
Answer» If the speed of the boat in still water is $x \frac{k m}{h}$ and speed of the stream is $y \frac{k m}{h}$ . S1 : upstream speed of the boat is $(x - y) \frac{k m}{h}$ S2 : downstream speed of the boat is $(x + y) \frac{k m}{h}$

928.

If the speed of the boat in still water is xkmh and speed of the stream is ykmh . S1 : upstream speed of the boat is (x−y)kmh S2 : downstream speed of the boat is (x+y)kmh

Answer»

If the speed of the boat in still water is $x \frac{k m}{h}$ and speed of the stream is $y \frac{k m}{h}$ .

S1 : upstream speed of the boat is $(x - y) \frac{k m}{h}$

S2 : downstream speed of the boat is $(x + y) \frac{k m}{h}$

Discussion

929.	32.Sa of cube is equal to sa of sphere. Find the ratio of their volumes
Answer» 32.Sa of cube is equal to sa of sphere. Find the ratio of their volumes

Discussion

930.	find the distance between the points(t1^3,root2t1) and (t2^3,-root2t2),if t1 andt2 are the roots of x^2-2root2 x+1=0
Answer» find the distance between the points(t1^3,root2t1) and (t2^3,-root2t2),if t1 and t2 are the roots of x^2-2root2 x+1=0

Discussion

931.	A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, the probability that it is rusted or is a nail is(a) 3/16(b) 5/16(c) 11/16(d) 14/16
Answer» A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, the probability that it is rusted or is a nail is (a) 3/16 (b) 5/16 (c) 11/16 (d) 14/16

Discussion

932.	If the ratio between 8 and 11 is the same as the ratio of 2x-y to x + 2y, find the value of 7x9y.
Answer» If the ratio between 8 and 11 is the same as the ratio of 2x-y to x + 2y, find the value of $\frac{7 x}{9 y}$ .

Discussion

933.	If Sn denote the sum of n terms of an A.P. with first term a and common difference d such that SxSkx is independent of x, then(a) d= a(b) d = 2a(c) a = 2d(d) d = −a
Answer» If S_n denote the sum of n terms of an A.P. with first term a and common difference d such that $\frac{S x}{S k x}$ is independent of x, then (a) d= a (b) d = 2a (c) a = 2d (d) d = −a

Discussion

934.	are the factors of the polynomial x2+2x−8.
Answer» are the factors of the polynomial $x^{2} + 2 x - 8$ .

Discussion

935.	How many two-digit numbers are divisible by 3? [CBSE 2012]
Answer» How many two-digit numbers are divisible by 3? [CBSE 2012]

Discussion

936.	Verify the following:(i) (0, 7, –10), (1, 6, –6) and (4, 9, –6) are vertices of an isosceles triangle.(ii) (0, 7, 10), (–1, 6, 6) and (–4, 9, –6) are vertices of a right-angled triangle.(iii) (–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are vertices of a parallelogram.(iv) (5, –1, 1), (7, –4,7), (1, –6,10) and (–1, – 3,4) are the vertices of a rhombus.
Answer» Verify the following: (i) (0, 7, –10), (1, 6, –6) and (4, 9, –6) are vertices of an isosceles triangle. (ii) (0, 7, 10), (–1, 6, 6) and (–4, 9, –6) are vertices of a right-angled triangle. (iii) (–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are vertices of a parallelogram. (iv) (5, –1, 1), (7, –4,7), (1, –6,10) and (–1, – 3,4) are the vertices of a rhombus.

Discussion

937.	consider a polynomial f(x)=ax^2+bx+c such that f(0)=4 when f(x) is divided by x+1, we get remainder as 4 and when it is divided by x+2, we get remainder as 6. find the values of a,b,c.
Answer» consider a polynomial f(x)=ax^2+bx+c such that f(0)=4 when f(x) is divided by x+1, we get remainder as 4 and when it is divided by x+2, we get remainder as 6. find the values of a,b,c.

Discussion

938.	In the given figure, O is the centre of the circle. PA and PB. Show that AOBP is a cyclic quadrilateral [CBSE 2014]
Answer» In the given figure, O is the centre of the circle. PA and PB. Show that AOBP is a cyclic quadrilateral [CBSE 2014]

Discussion

939.	______ is a line that touches a circle at only one point, and ______ is a line that intersects a circle at two distinct points.
Answer» ______ is a line that touches a circle at only one point, and ______ is a line that intersects a circle at two distinct points.

Discussion

940.	Question 3The following table gives production yield per hectare of wheat of 100 farms of a village. Production yield (in kg/ha)50−5555−6060−6565−7070−7575−80Number of farms2812243816Change the distribution to a more than type distribution and draw its ogive.
Answer» Question 3 The following table gives production yield per hectare of wheat of 100 farms of a village. $\begin{matrix} P r o d u c t i o n y i e l d (i n k g / h a) & 50 - 55 & 55 - 60 & 60 - 65 & 65 - 70 & 70 - 75 & 75 - 80 N u m b e r o f f a r m s & 2 & 8 & 12 & 24 & 38 & 16 \end{matrix}$ Change the distribution to a more than type distribution and draw its ogive.

Discussion

941.	If the linear equation y=7x−4 is written in standard form, the standard form being ax+by+c=0, then what are the possible value of a,b,c?
Answer» If the linear equation $y = 7 x - 4$ is written in standard form, the standard form being $a x + b y + c = 0,$ then what are the possible value of $a, b, c$ ?

Discussion

942.	The probability of getting an ever number, when a die is thrown once, is:
Answer» The probability of getting an ever number, when a die is thrown once, is:

Discussion

943.	Why a quadratic equation is in form- xsquare -(alpha +beta)x +alphabeta
Answer» Why a quadratic equation is in form- xsquare -(alpha +beta)x +alphabeta

Discussion

944.	Solve each of the following systems of equations by using the method of cross multiplication: 2x+5y=1,2x+3y=3.
Answer» Solve each of the following systems of equations by using the method of cross multiplication: $2 x + 5 y = 1, 2 x + 3 y = 3.$

944.

Solve each of the following systems of equations by using the method of cross multiplication: 2x+5y=1,2x+3y=3.

Answer»

Solve each of the following systems of equations by using the method of cross multiplication:

$2 x + 5 y = 1, 2 x + 3 y = 3.$

Discussion

945.	If the sum of three consecutive terms of an increasing AP is 99 and the product of the first and third of these terms is 1025, then the third term is
Answer» If the sum of three consecutive terms of an increasing AP is 99 and the product of the first and third of these terms is 1025, then the third term is

Discussion

946.	Question 37(iv) A child's game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a triangle of red colour?
Answer» Question 37(iv) A child's game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a triangle of red colour?

Discussion

947.	A 1.6 m tall girl stands at a distance of 3.2 m from a lamp-post and casts a shadow of 4.8 m on the ground. Find the height of the lamp-post by using (i) trignometric ratios (ii) property of similar triangles.
Answer» A 1.6 m tall girl stands at a distance of 3.2 m from a lamp-post and casts a shadow of 4.8 m on the ground. Find the height of the lamp-post by using (i) trignometric ratios (ii) property of similar triangles.

Discussion

948.	ΔABC is right angled at C with sides AB = 10 cm and AC = 6 cm. Find cosB.
Answer» $Δ A B C$ is right angled at C with sides AB = 10 cm and AC = 6 cm. Find cosB.

Discussion

949.	48. A wire of length 20m is bent in form of a rectangle of maximum area and minimmun area.Now if length and breadth are natural number then find
Answer» 48. A wire of length 20m is bent in form of a rectangle of maximum area and minimmun area.Now if length and breadth are natural number then find

Discussion

950.	Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape formed.
Answer» Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape formed.

Discussion

Explore topic-wise InterviewSolutions in .

Two triangles are said to be similar, if the corresponding sides are___ and the corresponding angles are___.

Question 3 (iii)The points A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of Δ ABC.Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ:QE = 2:1 and CR:RF = 2:1.

Rationalise the denominator and simplify(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

If the difference of mode and median of a data is 24, then the difference of median and mean is(a) 12(b) 24(c) 8(d) 36

Question 5A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60∘. Find the length of the string, assuming that there is no slack in the string.

The value of (1 - Cos A)(1 + Cos A)(cosec2A) is __

The shadow of a tower, when the angle of elevation of the sun is 45°, is found to be 10 m longer than when it was 60°. Find the height of the tower.

Find the H.C.F. of (3m3−12m2+21m−18) and (6m3−30m2+60m−48) by using the division method.

If p(x)=x−x2−2,then find p(1).

The length of the diagonal of a square is 102cm. Its area is(a) 200 cm2(b) 100 cm2(c) 150 cm2(d) 1002 cm2

Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that APAB=35. [CBSE 2011]

Question 97How many cubes each of side 0.5 cm are required to build a cube of volume of 8 cm3?

In figure, Point G is the point of concurrence of the medians of △PQR. If GT = 2.5, find the lengths of PG and PT.

Two cubes have their volumes in the ratio 1 : 27. What is the ratio of their surface areas?

in triangle PQR right angled at Q, PQ=QR, if QS is perpendicular to PR and QS=4cm, then the perimeter of triangle PQR is

AB is a diameter of a circle and AC is its chord such that ∠BAC = 30°. If the tangent at C intersects AB extended at D, then BC = ________.

If arc ABC=130∘ and arc CDE=110∘, then the measure of arc ACE is equal to?

Solve the following quadratic equations by factorization:abx2+b2-acx-bc=0

The sides of a right angled triangle are 5x, 4x and 3x units respectively. If the perimeter is 36 units, what is x? ___

A company manufactures cassettes. Its cost and revenue functions are C(x) = 26,000 + 30x and R(x) = 43x, respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realize some profit?

Determine the ratio in which the straight line x - y- 2 = 0 divides the line segment joining (3, -1) and (8, 9).

The following distribution gives daily income of 50 workers of a factory: Daily income(in ₹): 200 – 220 220 – 240 240 – 260 260 – 280 280 – 300 Number of workers: 12 14 8 6 10 Convert the distribution above to a 'less than type' cumulative frequency distribution and draw its ogive.

An object is thrown at an angle 'θ' with horizontal. If elevation angle of the object at its highest point as seen from the point ofprojection is †an^{-1}(1/2), then θ is equal to (1) 30^° (2) 45^° (3) 60^° (4) 37^°

(cosA−sinA+1)(cosA+sinA−1)= _________.

Solve for x: √x2+x−6−x+2=√x2−7x+10,xϵR

A solid cone of base radius 10 cm is cut into two parts through the midpoint of its height, by a plane parallel to its base. Find the ratio of the volumes of the two parts of the cone.

If the speed of the boat in still water is xkmh and speed of the stream is ykmh . S1 : upstream speed of the boat is (x−y)kmh S2 : downstream speed of the boat is (x+y)kmh

32.Sa of cube is equal to sa of sphere. Find the ratio of their volumes

find the distance between the points(t1^3,root2*t1) and (t2^3,-root2*t2),if t1 andt2 are the roots of x^2-2root2 x+1=0

A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, the probability that it is rusted or is a nail is(a) 3/16(b) 5/16(c) 11/16(d) 14/16

If the ratio between 8 and 11 is the same as the ratio of 2x-y to x + 2y, find the value of 7x9y.

If Sn denote the sum of n terms of an A.P. with first term a and common difference d such that SxSkx is independent of x, then(a) d= a(b) d = 2a(c) a = 2d(d) d = −a

are the factors of the polynomial x2+2x−8.

How many two-digit numbers are divisible by 3? [CBSE 2012]

consider a polynomial f(x)=ax^2+bx+c such that f(0)=4 when f(x) is divided by x+1, we get remainder as 4 and when it is divided by x+2, we get remainder as 6. find the values of a,b,c.

In the given figure, O is the centre of the circle. PA and PB. Show that AOBP is a cyclic quadrilateral [CBSE 2014]

______ is a line that touches a circle at only one point, and ______ is a line that intersects a circle at two distinct points.

Question 3The following table gives production yield per hectare of wheat of 100 farms of a village. Production yield (in kg/ha)50−5555−6060−6565−7070−7575−80Number of farms2812243816Change the distribution to a more than type distribution and draw its ogive.

If the linear equation y=7x−4 is written in standard form, the standard form being ax+by+c=0, then what are the possible value of a,b,c?

The probability of getting an ever number, when a die is thrown once, is:

Why a quadratic equation is in form- xsquare -(alpha +beta)x +alphabeta

Solve each of the following systems of equations by using the method of cross multiplication: 2x+5y=1,2x+3y=3.

If the sum of three consecutive terms of an increasing AP is 99 and the product of the first and third of these terms is 1025, then the third term is

Question 37(iv) A child's game has 8 triangles of which 3 are blue and rest are red, and 10 squares of which 6 are blue and rest are red. One piece is lost at random. Find the probability that it is a triangle of red colour?

A 1.6 m tall girl stands at a distance of 3.2 m from a lamp-post and casts a shadow of 4.8 m on the ground. Find the height of the lamp-post by using (i) trignometric ratios (ii) property of similar triangles.

ΔABC is right angled at C with sides AB = 10 cm and AC = 6 cm. Find cosB.

48. A wire of length 20m is bent in form of a rectangle of maximum area and minimmun area.Now if length and breadth are natural number then find

Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape formed.

Two triangles are said to be similar, if the corresponding sides are_ and the corresponding angles are_.

find the distance between the points(t1^3,root2t1) and (t2^3,-root2t2),if t1 andt2 are the roots of x^2-2root2 x+1=0

is a line that touches a circle at only one point, and is a line that intersects a circle at two distinct points.