The equation of the circle passing through (0, 0) and cutting orthogonally the circles x²+y²+6x-15=0, x²+y²-8x+10=0 is

The equation of the circle passing through the points of intersection of the circle x²+y²-2x+4y-20=0, the line 4x-3y-10=0 and the point (3, 1) is

The equation of the circle touching the line 3x-4y-15=0 and belonging to the coaxal system having limiting points (2, 0), (-2, 0) is

The locus of the centre of the circles which touches externally the circle x²+y²-6x-6y+14=0 and also touches the y-axis is given byt the equation

The parametric equations of circle (x-3)²+(y-2)²=100 are

The point (-1, 0) lies on the circle x²+y²-4x+8y+k=0. The radius of the circle

The lengths of the chords of the circle x²+y²-2x-6y-15=0 which make an angle of 60⁰ at (1, 3) and the locus of the midpoints of all such chords are

The shortest distance from (-2, 14) to the circles x²+y²-6x-4y-12=0 is

If the distances from the origin to the centres of three circles x²+y²-2k, x=c² (i=1,2,3),are in G.P, then the lengths of the tangents drawn to them from any point on the circle x² + v² = c² are in

If α, β are the roots of x²+ ax+b=0 and γ, δ are the roots y²+cx+d=0 then the equation of the circle having the line joining (α, γ), (β, δ) as diameter is