If `y = 2x + c` neither cuts the circle `(x - 2)^2 + (y - 3)^2 = 4` nor the ellipse `x^2 + 6y^2 = 6,` then the range of c is

The circle x^2 + y^2 - 4x + 6y + c = 0 touches x axis if

If the circle x^(2) + y^(2) = 9 touches the circle x^(2) + y^(2) + 6y + c = 0 internally, then c is equal to

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

If the circle x^(2) + y^(2) + 8x - 4y + c = 0 touches the circle x^(2) + y^(2) + 2x + 4y - 11 = 0 externally and cuts the circle x^(2) + y^(2) - 6x + 8y + k = 0 orthogonally then k =

The length of common chord of the circles x^2 + y^2 - 6x - 4y + 13 - c^2 = 0 and x^2 + y^2 -4x - 6y + 13 -c^2 = 0 is

The locus of the centre of circle which cuts the circles x^2 + y^2 + 4x - 6y + 9 =0 and x^2 + y^2 - 4x + 6y + 4 =0 orthogonally is

If y+c=0 is a tangent to the circle x^(2)+y^(2)-6x-2y+1=0 at (a, 4), then