For what value of `k` is the circle `x^2 + y^2 + 5x + 3y + 7 = 0` and `x^2 + y^2 - 8x + 6y + k = 0` cut each other orthogonally.

Show that the circles x^2 + y^2 - 2x-6y-12=0 and x^2 + y^2 + 6x+4y-6=0 cut each other orthogonally.

Show that the circles x^(2) + y^(2) + 2 x -6 y + 9 = 0 and x^(2) +y^(2) + 8x - 6y + 9 = 0 touch internally.

Two circles x^(2) + y^(2) + ax + ay - 7 = 0 and x^(2) + y^(2) - 10x + 2ay + 1 = 0 will cut orthogonally if the value of a is

If the circle x^2 + y^2 + 2x - 2y + 4 = 0 cuts the circle x^2 + y^2 + 4x - 2fy +2 = 0 orthogonally, then f =

For what value of k will the line 4x + 3y + k = 0 touch the circle 2x^(2) + 2y^(2) = 5x

Find the equation of circle passing through the origin and cutting the circles x^(2) + y^(2) -4x + 6y + 10 =0 and x^(2) + y^(2) + 12y + 6 =0 orthogonally.

Circles x^(2) + y^(2) - 2x = 0 and x^(2) + y^(2) + 6x - 6y + 2 = 0 touch each other extermally. Then point of contact is

If the circles x^(2) + y^(2) = k and x^(2) + y^(2) + 8x - 6y + 9 = 0 touch externally, then the value of k is

The equation of the circle passing through the point of intersection of the circles x^2 + y^2 - 6x + 2y + 4 = 0 and x^2 + y^2 + 2x - 6y - 6=0 and having its centre on y=0 is : (A) 2x^2 + 2y^2 + 8x + 3 = 0 (B) 2x^2 + 2y^2 - 8x - 3 = 0 (C) 2x^2 + 2y^2 - 8x + 3 = 0 (D) none of these

For what value of k is the line x-y+2+k(2x+3y)=0 parallel to the line 3x+y=0 ?