﻿ Find the equation of the circle passing through the point of intersection of the circles x2 + y2 – 6x + 2y + 4 = 0, x2 + y2 + 2x – 4y – 6 = 0 and with its centre on the line y = x. : Kaysons Education

Find The Equation Of The Circle Passing Through The Point Of Intersection Of The Circles x2 + y2 – 6x + 2y + 4 = 0, x2 + y2 + 2x – 4y – 6 = 0 And With Its Centre On The Line y = x.

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Question

Solution

Correct option is

7x2 + 7y2 – 10x – 10y – 12 = 0

Equation of any circle through the points of intersection of given circles is

(x2 + y2 – 6x + 2y + 4) + λ(x2 + y2 + 2x – 4y – 6) = 0

⇒      x2(1 + λ) + y2(1+ λ) – 2x(3 – λ) + 2y(1 – 2λ) + (4 – 6λ) = 0

∴ Substituting the value of λ = 4/3 in (1), we get the required equation is

7x2 + 7y2 – 10x – 10y – 12 = 0

SIMILAR QUESTIONS

Q1

Find the equation of the chord x2 + y2 – 6x + 10y – 9 = 0 which is bisected at (–2, 4).

Q2

Find the middle point of the chord intercepted on line lx + my + n = 0 by the circle x2 + y2 = a2.

Q3

Find the locus of middle points of chords of the circle x2 + y2 = a2, which subtend right angle at the point (c, 0).

Q4

Find the equations of the tangents from the point A(3, 2) to the circle x2y2 + 4x + 6y + 8 = 0 .

Q5

If two tangents are drawn from a point on the circle x2 + y2 = 50 to the circle x2 + y2 = 25 then find the angle between the tangents.

Q6

Find the equation of the diameter of the circle

x2 + y2 + 2gx + 2fy + c = 0 which corresponds to the chord ax = by + d= 0.

Q7

Find the locus of the pole of the line lx + my + n = 0 with respect to the circle which touches y-axis at the origin.

Q8

Examine if the two circles x2 + y2 – 2x – 4y = 0 and x2 + y2 – 8y – 4 = 0 touch each other externally or internally.

Q9

Find the equation of the circle passing through (1, 1) and the points of intersection of the circles

x2 + y2 + 13x – 3y = 0 and 2x2 + 2y2 + 4x – 7y – 25 = 0.

Q10

Find the equation of the circle passing through the points of intersection of the circles x2 + y2 – 2x – 4y – 4 = 0 and x2 + y2 – 10x – 12y + 40 = 0 and whose radius is 4.