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=

The equation to the locus of the midpoint of the chords of the circle x²+y²=r² having a constant length 2l is

Consider the circles x²+(y-1)²=9, (x-1)²+y²=25. They are such that

The parametric equations of circle x²+y²+8x-6y=0 are

The centre of the circle passing through the points (a, b), (a, -b), (a+b, a-b) is

The point diametrically opposite to the point P(1, 0) on the circle x²+y²+2x+4y-3=0 is

If the lines 3x + 4y - 14 = 0 and 6x + 8y + 7 = 0 are both tangents to a circle, then its radius is