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

The circle described on the line joining the points (0, 1), (a, b) as diameter cuts the x-axis in points whose abscissa are roots of the equation

If the length of the tangent from (h, k) to the circle x²+y²=16 is twice the length of the tangent from the same point to the circle x²+y²+2x+2y=0, then

The equation of the circle concentric with  circlex²+y²-6x+12y+15=0 and of double its area is