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

The least distance of the line 8x-4y+73=0 from the circle 16x²+16y²+48x-8y-43=0 is

The equation of the circle with centre (-1, 1) and touching the circle x²+y²-4x+6y-3=0 externally is

The orthocentre of triangle formed by the lines x + 3y = 10 and 6x² + xy - y² = 0 is:

B and C are two points on the circle x²+y²=a². From a point A(b, c) on that circle AB=AC=d. The equation to Bc is

The locus of the centre of the circles which touché both the circles x²+y²=a² and x²+y²=4ax externally has the equation