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

The equation of the circle passing through the points of intersection of the circlesx2+y2=5, x²+y²+12x+8y-33=0 and touching x-axis is

If 4y=x+7 is diameter of the circumscribing circle of the rectangle ABCD and A(-3, 4), B(5, 4), then the area of the rectangle is

The polar of the point(2t, t-4) w.r.t the circle x²+y²-4x-6y+1=0 passes through the point

The locus of midpoints of chords of the circle x²+y²=2r² subtending a right angle at the centre of the circle is

The centres of the circles are (a, c) and (b, c) and their radical axis is the y-axis. The radius of one of the circle is r. The radius of the other circle is

The tangents drawn from the origin to the circle x²+y²-2rx-2hy+h²=0 are perpendicular if

If x²+y²-2x+3y+k=0 and  x²+y²+8x-6y-7=0 cut each orthogonally, the value of k must be