The number of common tangents to the circles x²+y²+2x+8y-23=0, x²+y²-4x-10y+19=0 is

If the lines 2x-3y=5 and 3x-4y=7 are two diameters of a circle of radius 7, then the equation of the circle is

The centre of the circle x²+y²-4x-2y-4=0 is

If the two circles (x-2)²+(y-3)²=r²and x²+y²-10x+2y+17=0 intersect in two distrinct points then

The limiting points of coaxal system x²+y²+11x-5y-2+λ(x-y-1)=0 is

The equation of the circle passing through the point of intersection of the circles x²+y²-3x-6y+8=0, x²+y²-2x-4y+4=0 and touching the line x+2v=5 is

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