let `S_1`=`x^2+y^2-4x-8y+4=0` and `S_2` be its image in the line `y=x` find the equation of circle touching `y=x` at (1,1) and its radical axes with `S_2` passes through the centre of `S_1`

Find the equation of the circle with centre at (1,-2) and passing through the centre of the circle x^2+y^2-4x+1=0

The equation of the circle having the lines y^(2) – 2y + 4x – 2xy = 0 as its normals & passing through the point (2, 1) is

Find the equation of the circle which passes through the points (1, 3 ) and (2, - 1 ) , and has its centre on the line 2x + y - 4 = 0

Let S_(1): x^(2)+y^(2)=9 and S_(2) : (x-2)^(2)+y^(2)=1 . Then the locus of centre of a variable circle S which touches S_1 internally and S_2 externally always passes through the points:

(i) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 6x + 12y + 15 = 0 and of double its radius. (ii) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 2x - 4y + 1 = 0 and whose radius is 5. (iii) Find the equation of the cricle concentric with x^(2) + y^(2) - 4x - 6y - 3 = 0 and which touches the y-axis. (iv) find the equation of a circle passing through the centre of the circle x^(2) + y^(2) + 8x + 10y - 7 = 0 and concentric with the circle 2x^(2) + 2y^(2) - 8x - 12y - 9 = 0 . (v) Find the equation of the circle concentric with the circle x^(2) + y^(2) + 4x - 8y - 6 = 0 and having radius double of its radius.

Find the equation of the circle , centred at (-1,4) , which touches the circle x^(2) + y^(2) - 6x - 2y + 1 = 0 externally

Find the equation of the circle passing through the point (-1,3) and having its centre at the point of intersection of the lines x-2y=4 and 2x+5y+1=0

For the circles S_1: x^2 + y^2-4x-6y-12 = 0 and S_2 : x^2 + y^2 + 6x + 4y-12=0 and the line L.:x+y=0 (A) L is common tangent of S_1 and S_2 (B) L is common chord of S_1 and S_2 (C) L is radical axis of S_1 and S_2 (D) L is perpendicular to the line joining the cente of S_1 & S_2

The equation of the circle passing through the point (1,-2) and having its centre on the line 2x-y-14=0 and touching the line 4x+3y-23=0 is

Find the equation of the circle which cuts the circle x^(2)+y^(2)+5x+7y-4=0 orthogonally, has its centre on the line x=2 and passes through the point (4,-1).