The equation of three circles are given `x^2+y^2=1,x^2+y^2-8x+15=0,x^2+y^2+10 y+24=0` . Determine the coordinates of the point `P` such that the tangents drawn from it to the circle are equal in length.

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

If the straight line x - 2y + 1 = 0 intersects the circle x^2 + y^2 = 25 at points P and Q, then find the coordinates of the point of intersection of the tangents drawn at P and Q to the circle x^2 + y^2 = 25 .

Show that the circles x^2+y^2-10 x+4y-20=0 and x^2+y^2+14 x-6y+22=0 touch each other. Find the coordinates of the point of contact and the equation of the common tangent at the point of contact.

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

The tangent to the circle x^2+y^2=5 at (1,-2) also touches the circle x^2+y^2-8x+6y+20=0 . Find the coordinats of the corresponding point of contact.

Find the equation of the normals to the circle x^2+y^2-8x-2y+12=0 at the point whose ordinate is -1

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 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