The condition so that the line `(x + g) cos theta + (y+f) sintheta = k` is a tangent to ` x^2 + y^2 + 2gx+2fy+c =0` is

The condition that the line (x + g) cos theta + ( y +f ) sin theta = k is a tangent to x^2+y^2 +2gx +2fy +c=0 :

The condition so that the line (x+g)cos theta+(y+f)sin theta=k is a tangent to x^(2)+y^(2)+2gx+2fy+c=0 is

Find the conditions that the tangents drawn from the exteriorpoint (g,f) to S= x^(2) + y ^(2) + 2gx + 2fy + c=0 are perpendicular to each other.

Find the condition for the line Ix+my+ n = 0 is a normal to the circle x^2 + y^2 + 2gx + 2fy + c = 0 .

Fing the condition that the tangents drawn from the exterior point (g, f) to S -= x^(2) + y^(2) + 2 gx + 2fy + c=0 are perpen- dicular to each other.

The condition that the pair of tangents drawn from the origin to the circle x^(2)+y^(2)+2gx+2fy+c=0 may be at right angles is

If the circle x ^(2) + y^(2) + 2gx + 2fy+ c=0 touches X-axis, then

The condition that the pair of tangents drawn from origin to the circle x^(2)+y^(2)+2gx+2fy+c=0 may be at right angle is