A. 9a2=r2

B. 9r2=a2

C. r2=a2

D. none

P(-2, -1) and (0, -3) are the limiting points of a coaxal system of which C= x^{2}+y^{2}+5x+y+4=0 is a member. The circle S= x^{2}+y^{2}-4x-2y-15=0 is orthogonal to the circle C. The point where the polar P cuts the circle S is

A tangent to the circle x^{2}+y^{2}=4 meets the coordinate axes at P and Q. The locus of mindpoint of PQ is

The condition that the circles (x-α)^{2}+(y-β)^{2}=r^{2}, (x-β)^{2}+(y-α)^{2}=r^{2} may touch each other is

The length of the chord of contact of (-2, 3) with respect to the circle x^{2}+y^{2}-2x+4y+1=0 is

From the origin chords are drawn to x^{2}+y^{2}-2y=0. The locus of the middle points of these chords is