Home
Class 12
MATHS
Find the equation of the circle passing ...

Find the equation of the circle passing throught (1,1) and the points of intersection of the circles `x^(2)+y^(2)+13x-3y=0` and `2x^(2)+2y^(2)+4x-7y-25=0`

Text Solution

Verified by Experts

Equation of the circle passing through the points of intersection of the given circles is
`(x^(2)+y^(2)+13x-3y)+lambda(2x^(2)+2y^(2)+4x-7y-25)=0` (1)
If this circle passes through the point (1,1), then
`(1+1+13-3)+lambda(2+2+4-7-25)=0`
`implies lambda = 1//2`
Substituting `lambda =1//2` in (1), we get the equation of the required circle as `4x^(2)+4y^(2)+30x-13y-25=0`.
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Show that the equation of the circle passing through (1, 1) and the points of intersection of the circles x^2+y^2+13 x-3 y=0 and 2x^2+2y^2+4x-7y-25=0 is 4x^2+4y^2+30 x-13 y-25=0.

The equation of the line passing through the points of intersection of the circles 3x^2 +3y^2-2x + 12y-9=0 and x^2+y^2+6x+2y-15=0 is

Find the point of intersection of the circle x^2+y^2-3x-4y+2=0 with the x-axis.

Find the equation of the smallest circle passing through the intersection of the line x+y=1 and the circle x^2+y^2=9

The equation of the circle passing through the point of intersection of the circles x^2+y^2-4x-2y=8 and x^2+y^2-2x-4y=8 and the point (-1,4) is (a) x^2+y^2+4x+4y-8=0 (b) x^2+y^2-3x+4y+8=0 (c) x^2+y^2+x+y=0 (d) x^2+y^2-3x-3y-8=0

Find the equation of radical axis of the circles x^(2)+y^(2)-3x+5y-7=0 and 2x^(2)+2y^(2)-4x+8y-13=0 .

Find the equations of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2

Find the equation of the lines passing through the point of intersection lines 4x-y+3=0 and 5x+2y+7=0 Parallel to x-y+5=0

find the equation of the circle with centre (2,3) and passing through the intersection of the lines 3x -2y -1=0 and 4x + y -27 =0 ..