The equation of one tangent to the circle with Centre(2,-1) from the origin is 3x + y = 0, then the equation of the other tangent through the origin is

The equation to the circle which is such that the lengths of the tangents to it from the points (1,0), (2,0) and (3,2)are 1,√7, √2, respectively is

The locus of the centre of the circles which touché both the circles x²+y²=a² and x²+y²=4ax externally has the equation

The locus of the centre of the circle which cuts the circles x²+y²+4x-6y+9=0 and x²+y²-4x+6y+4=0 orthogonally is

A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is

The pole of the line ax+by+3a²+3b²=0 w.r.t to the circle x²+y²+2ax+2by-a²-b²=0 is

The circle with centre on the line 2x-2y+9=0 and cutting the circles x²+y²=4 orthogonally, passes through the fixed points

The lengths of the tangents from any point on the circle 15x²+15y²-48x+64y=0 to the two circles 5x²+5y²-24x+32y+75=0, 5x²+5y²-48x+64y+300=0 are in the ratio

The equation of the common chord of the two circles x²+y²+2x+3y+1=0, x²+y²+4x+3y+2=0 is

The point  (3,  1) is a point on a circle C with centre  (2,  3) and  C is  orthogonal  to x²+y²=8. The conjugate  point  of (3,  1) w.r. to  x² + y² =8 which lies  on C is