Find the locus of the centers of the circles `x^2+y^2-2ax-2b y+2=0` , where `a` and `b` are parameters, if the tangents from the origin to each of the circles are orthogonal.

Find the locus of the midpoint of the chord of the circle x^2+y^2-2x-2y=0 , which makes an angle of 120^0 at the center.

Find the angle between the two tangents from the origin to the circle (x-7)^2+(y+1)^2=25

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

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.

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

Find the equations to the common tangents of the circles x^2+y^2-2x-6y+9=0 and x^2+y^2+6x-2y+1=0

Find the locus of the center of the circle touching the circle x^2+y^2-4y=4 internally and tangents on which from (1, 2) are making of 60^0 with each other.

Find the equation of the tangent to the circle x^2 + y^2 - 2ax - 2ay + a^2 = 0 which makes with the coordinate axes a triangle of area a^2.

The equation of the locus of the middle point of a chord of the circle x^2+y^2=2(x+y) such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally inclined to the x-axis is x+y=2 (b) x-y=2 2x-y=1 (d) none of these