Find the length of the chord of contact with respect to the point on the director circle of circle `x^2+y^2+2a x-2b y+a^2-b^2=0` .

The director circle of the ellispe x^(2)/9 + y^(2)/5 = 1

If the radius of the circumcircle of the triangle TPQ, where PQ is chord of contact corresponding to point T with respect to circle x^2 +y^2- 2x +4y -11=0 , is 6 units, then minimum distances of T from the director circle of the given circle is

If the radius of the circumcircle of the triangle TPQ, where PQ is chord of contact corresponding to point T with respect to circle x^2 +y^2- 2x +4y -11=0 , is 6 units, then minimum distances of T from the director circle of the given circle is

Find the middle point of the chord of the circle x^2+y^2=25 intercepted on the line x-2y=2

Find the length of the common chord of the parabola y^2=4(x+3) and the circle x^2+y^2+4x=0 .

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

Find the point of intersection of the circle x^2+y^2-3x-4y+2=0 with the x-axis.

Examine the position of the point (-2,-3) with respect to the circle x^(2)+y^(2)-x-y-7=0 .

Find the locus of a point which moves so that the ratio of the lengths of the tangents to the circles x^2+y^2+4x+3=0 and x^2+y^2-6x+5=0 is 2: 3.

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.