The locus of the point of intersection of two perpendicular tangents to the circle x²+y²=a², x²+y²=b² is

The equation of the image of the circle x²+y²-6x-4y+12=0 by the line mirror x+y-1=0 is

The inverse point of (1, 2) w.r.t the circle x²+y²=25 is (5, k), then k=

If the points (2, 3), (0, 2), (4, 5) and (0, t) are concyclic, then t=

For the circle x²+y²-4x-2y-36=0, the point (3, 5)

The polars of two points A(1, 3) and B(2, -1) w.r.to the circle x²+y²=9 intersect at C. Then the polar of C w.r.to the circle is

The equation of the chord of the circle x²+y²-4x+6y-3=0 having (1, -2) as its midpoint is

From the point A(0,3) on the circle x²+4x+(y-3)²=0, a chord, AB is drawn and extended to a point P, such that AP = 2AB. The locus of P is

If α,β,γ are the roots of x³-x²+33x+5=0 and A=s₁,B=s₂,C=s₃ then the descending order of A,B,C is

If the circles x²+y²+2x-2y+4=0 cuts the circle x²+y²+4x-2fy+2=0 orthogonally, then f=