Equation of the circle passing through (2, 0) and whose radical axis w. r. to the circle x²+y²=1 is at x=1/2 is

If the tangent from a point P to the circle x²+y²=1 is perpendicular to the tangent from P to the circle x²+y²=3, then the locus of P is

The locus of the poles of the line 2x-3y-4=0 w.r.t the circle x²+y²+2λx-16=0 is

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