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

The polar of given point with respect to any one of the circles x²+y²-2kx+c²=0, (k is a variable) always passes through a fixed point whatever be the value of k is

The locus of the foot of the perpendicular drawn from the origin to any chord of the circle x²+y²+2gx+2fy+c=0 which substends a right angle at the origin is