If the line x+y+1=0 touches the circle x²+y²-3x+7y+14=0, then the point of contact is

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

Equation x²+2ax-b²=0 has real roots α, β and equation x²+2px-q²=0 has real roots γ, δ. If circle C is drawn with the points (α, γ), (β, δ) as extremities of a diameter, then the equation of C is

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