The equation of the circle with centre (4, 3) and touching circle x2 +

1.	The equation of the circle with centre (4, 3) and touching circle x2 + y2 = 1 is(A) x2 + y2 - 8x - 6y + 11 = 0(B) x2 + y2 - 8x - 6y + 9 = 0 (C) x2 + y2 - 8x - 6y - 9 = 0 (D) x2 + y2 - 8x - 6y - 11 = 0
Answer» Correct option (b,d) Explanation : Since (3, 4) lies outside the circle x² + y² = 1, one circle has the external contact with x² + y² = 1 and the other circle has the internal contact. O = (0, 0) and r₁ = 1. Let A = (4, 3) and r₂ be the radius of the required circle OA = 5. Case 1: r₂ = 5 - 1 = 4 (i.e. external contact). Hence, the required circle is (x - 4)² + (y - 3)² = 16 ⇒ x² + y² - 8x -6y + 9 = 0 Case 2: r₂ = 5 + 1 = 6 (i.e. internal contact). Hence, the required circle is (x - 4)² + (y - 3)² = 36 ⇒ x² + y² - 8x - 6y -11 = 0

The equation of the circle with centre (4, 3) and touching circle x2 + y2 = 1 is(A) x2 + y2 - 8x - 6y + 11 = 0(B) x2 + y2 - 8x - 6y + 9 = 0 (C) x2 + y2 - 8x - 6y - 9 = 0 (D) x2 + y2 - 8x - 6y - 11 = 0

Answer»

Correct option (b,d)

Explanation :

Since (3, 4) lies outside the circle x² + y² = 1, one circle has the external contact with x² + y² = 1 and the other circle has the internal contact. O = (0, 0) and r₁ = 1. Let A = (4, 3) and r₂ be the radius of the required circle OA = 5.

Case 1: r₂ = 5 - 1 = 4 (i.e. external contact). Hence, the required circle is

(x - 4)² + (y - 3)² = 16

⇒ x² + y² - 8x -6y + 9 = 0

Case 2: r₂ = 5 + 1 = 6 (i.e. internal contact). Hence, the required circle is

(x - 4)² + (y - 3)² = 36

⇒ x² + y² - 8x - 6y -11 = 0

Discussion

No Comment Found

Related InterviewSolutions

The number of integer values of k for which the chord of the circle x2 + y2 = 125 passing through the point P(8, k) and is bisected at the point P(8, k) with integer slope is ......
C1 is a circle with centre at A and radius 2. C2 is a circle with centre at B and radius 3. The distance AB is 7. If P is the point of intersection of a transverse common tangent with line AB, then the distance AP is(a) 14/5(b) 7/3(c) 9/4(D) 8/3
Find the equation of a circle that passes through the point (1, 2) which bisects the circumference of the circle x2 + y2 = 9 and is orthogonal to the circle x2 - y2 − 2x + 8y − 7 = 0.
Find the equation of the circle passing through the origin which is cutting the chord of equal length √2 on the lines y = x and y = −x.
A and B are two fixed points in a plane and k > 0, Then the locus of P such that PA:PB = k : 1 is a circle, provided k is not equal to ....
A rational point in an analytical plane means that both the coordinates of the point are rational numbers. Then the maximum number of rational points on a circle C with centre (0,√2) is ....
The line λx - y + 1 = 0 cuts the coordinate axes at points P and Q. The line x - 2y + 3 = 0 intersects the coordinate axes at points R and S. If P, Q, R and S are concyclic, then the value of K is .....
Point P is on the circle x2 + y2 − 2ax = 0. A circle is drawn on OP as diameter where O is the origin. As P moves on the circle, find the locus of the centre of the circle.
Determine the equation of the circle which touches the line y = x at the origin and bisects the circumference of the circle x2 + y2 + 2y − 3 = 0.
Tangents are drawn from any point on the circle x2 + y2 + R2 to the circle x2 + y2 + r2. If the line joining the points of intersection of these tangents with the first circle also touches the second, then R:r is(A) 2:1 (B) 1:2(C) 3:1(D) √2 : 1