Find the equation of the circle passing through the points A(0, 1), B(

1.	Find the equation of the circle passing through the points A(0, 1), B(2, 3) and C(−2, 5).
Answer» Let S ≡ x² + y² + 2gx + 2fy + c = 0 be the circle passing through points A, B and C. Therefore 2f + c = -1 4g + 6f + c = -13 -4g + 10f + c = -13 -4g +10f + c = -29 .......(1) Solving the system of equations provided in Eq. (1), we get get g = 1/3, f = −10/3 and c = 17/3 so that the equation of the circle is x¹ + y² + 2/3x - 20/3y + 17/3 = 0 3x² + 3y² + 2x - 20y + 17 = 0 Note: Under the given hypothesis, to find the equation of the circle, it is sufficient if we find its centre and radius or assume the circle as x² + y²+ 2gx + 2fy + c = 0 and find the values of g, f and c.

Find the equation of the circle passing through the points A(0, 1), B(2, 3) and C(−2, 5).

Answer»

Let S ≡ x² + y² + 2gx + 2fy + c = 0 be the circle passing through points A, B and C. Therefore

2f + c = -1

4g + 6f + c = -13

-4g + 10f + c = -13

-4g +10f + c = -29 .......(1)

Solving the system of equations provided in Eq. (1), we get get g = 1/3, f = −10/3 and c = 17/3 so that the equation of the circle is

x¹ + y² + 2/3x - 20/3y + 17/3 = 0

3x² + 3y² + 2x - 20y + 17 = 0

Note: Under the given hypothesis, to find the equation of the circle, it is sufficient if we find its centre and radius or assume the circle as x² + y²+ 2gx + 2fy + c = 0 and find the values of g, f and c.

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