If a, b, c are the lengths of tangents from (0, 0) to the circle x²+y²-3x-4y+1=0, x²+y²+4x-6y+4=0, x²+y²-6x-12y+9=0 then the ascending order of a, b, c is

The two circles (x-a)²+(y-b)²=c and (y-b)²+x²=4c have only one real common tangent then

The locus of the point whose shortest distance from the circle x²-2x+6y-6=0 is equal to its distance from the line x-3=0 is

A=(cosθ, sinθ) and B==(sinθ, -cosθ) are two points. The locus of the centroid of ΔOAB where O is the origin is

The conjugate system of the coaxal system x²+y²+2ax+2by+2λ(ax-by)=0, λ is a parameter, is

The locus of the midpoint of the chord of the circle x²+y²-2x-2y-2=0, which makes an angle of 120⁰ at the centre is

Let A and B be two fixed points, If a perpendicular p is drawn from A to the polar of B with respect to the circle x²+y²=a² and perpendicular q is drawn from B to the polar of A then

The circle x²+y²=4 cuts the circle x²+y²-2x-4=0 at the points A and B. If the circle x²+y²-4x-k=0 passes through A and B then the value of k is

The equation of the circle passing through (-7, 1) and having centre at (-4, -3) is

The system of circles orthogonal to x²+y²+2x+4y+7=0 is a member, then the equation of the orthogonal system is