Find the equation of the circle which touches the line `x - y = 0` at origin and bisect the circumference of the circle `x^2 + y^2 + 2y - 3 = 0`.

Find the equation of the circle which touches the line x = 0, x = a and 3x + 4y + 5a = 0.

The equation of the circles which touch the x-axis at the origin and the line 4x-3y+24=0

Find the equation of the circle which touches the lines 4x-3y+10=0a n d4x-3y-30=0 and whose centre lies on the line 2x+y=0.

Find the equation of the circle which touches the lines 4x-3y+10=0 and 4x-3y-30=0 and whose centre lies on the line 2x+y=0 .

Find the equation of a circle, which touches the line x+ y = 5 at the point (-2, 7) and cuts the circle x^2+ y^2+ 4x - 6y +9 =0 orthogonally.

Find the equation of the family of circles touching the lines x^2-y^2+2y-1=0.

Find the equation of the family of circles touching the lines x^2-y^2+2y-1=0.

Find the equation of the circle which bisects the circumference of the circle x^(2) + y^(2) + 2y - 3 = 0 and touches the straight line y = x at the origin.

If the circle x^(2) + y^(2) + 6x - 2y + k = 0 bisects the circumference of the circle x^(2) + y^(2) +2x - 6y - 15 = 0 , then k =

If the circle x^2 + y^2 + 6x -2y + k = 0 bisects the circumference of the circle x^2 + y^2 + 2x- 6y-15=0 , then