If the two circle x²+y²+2gx+c=0 and x²+y²-2fy-c=0 have equal radius then locus of (g, f) is

The point (3, -4) lies on both the circles x²+y²-2x+8y+13=0 and x²+y²-4x+6+11=0. Then the angle between the circles is

The nearest point on the circle x²+y²-6x-4y-12=0 from (-5, 4) is

The equation of the tangents to a circle x²+y²-4x-6y-12=0 and parallel to 4x-3y=1 are

The equation of the chord of the circle x²+y²=25 with (1, -1) as the midpoint is

The equations to the direct common tangents to the circles x²+y²+22x-4y-100=0, x²+y²-22x+4y+100=0is

If the equation of the circle cutting the circle x²+y²+2x-4y+8=0 orthogonally and coaxal with the circles x²+y²+6x+4y-12=0, x²+y²-4x-6y-12=0 is x²+y²+2ax+2by+c=0 then the ascending order of a, b, c is

The equation of the circle with centre at (2,3) and touching x-axis is

The condition that the circles x²+y²+2ax+2by+c=0, x²+y²+2bx+2ay+c=0 to touch each other is

The number of common tangents that can be drawn to the circles x²+y²=1 and  x²+y²-2x-6y+6=0 is