Let AB be the chord 4x-3y +5 = 0 with respect to the circle x²+y²-2x+4y-20=0. If C= (7, 1), then the area of the triangle ABC is

The circles x²+y²=1 ,  x²+y²+6x-2y=1 and x²+y²-12x+4y=1 are such that

The polar of the point (1, -2) w.r.t the circles  x²+y²+6y+5=0 , x²+y²+2x+8y+5=0 are

The number of common tangents to the two circles x²+y²=4, x²+y²-8x+12=0 is

If (2, 6) is a centre of similitude for the-circles x²+y²=4 and x²+y²-2x-6y+9=0, the length of the common tangent of circles through it is

The radical axis of co-axial system of circle with the limiting points (1, 2) and (4, 3) is given by in equation

A tangent at a point on the circle x²+y²=a² intersects a concentric circle S at P and Q. The tangents to S at P and Q meet on the circle x²+y²=b². The equation to the circle S is

If (1, a), (b, 2) are conjugate points with respect to the circle x²+y²=25, then 4a+2b=

The equation of the circle cutting orthogonally circles x²+y²-4x+3y-1=0 and passing through the points (-2, 5), (0, 0) is

If the points (k, 1), (2, -3) are conjugate w.r.t x²+y²+4x-6y-12=0 then k=