Find the length of the tangent drawn from any point on the circle `x^2+y^2+2gx+2fy+c_1=0` to the circle `x^2+y^2+2gx+2fy+c_2=0`

Find the length of the tangent from (2,-3) to the circle x^(2) + y^(2) -8y -9y + 12=0

The equation of tangents drawn from the origin to the circle x^2+y^2-2rx-2hy+h^2=0

If the chord of contact of the tangents drawn from a point on the circle x^2+y^2=a^2 to the circle x^2+y^2=b^2 touches the circle x^2+y^2=c^2 , then prove that a ,b and c are in GP.

The length of the tangent from any point on the circle to the circle (x-3)^2 + (y + 2)^2 =5r^2 to the circle (x-3)^2 + (y + 2)^2 = r^2 is 4 units. Then the area between the circles is

If the length tangent drawn from the point (5, 3) to the circle x^2+y^2+2x+k y+17=0 is 7, then find the value of kdot

Find the length of the common chord of the circles x^2+y^2+2x+6y=0 and x^2+y^2-4x-2y-6=0

If the distances from the origin of the centers of three circles x^2+y^2+2lambdax-c^2=0,(i=1,2,3), are in GP, then prove that the lengths of the tangents drawn to them from any point on the circle x^2+y^2=c^2 are in GP.

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x-5y=20 to the circle x^2+y^2=9 is : (A) 20(x^2+y^2)-36+45y=0 (B) 20(x^2+y^2)+36-45y=0 (C) 20(x^2+y^2)-20x+45y=0 (D) 20(x^2+y^2)+20x-45y=0

Tangent is drawn at any point (x_1, y_1) other than the vertex on the parabola y^2=4a x . If tangents are drawn from any point on this tangent to the circle x^2+y^2=a^2 such that all the chords of contact pass through a fixed point (x_2,y_2), then (a) x_1,a ,x_2 in GP (b) (y_1)/2,a ,y_2 are in GP (c) -4,(y_1)/(y_2), (x_1//x_2) are in GP (d) x_1x_2+y_1y_2=a^2

Find the equation of tangent to the circle x^(2) + y^(2) + 2x -3y -8 = 0 at (2,3)