If the circle $x^{2}+y^{2}-2 g x+6 y-19 c=0, g, c \in \mathbb{R}$ passes through the point $(6,1)$ and its centre lies on the line $x-2 c y=8$, then the length of intercept made by the circle on $x$-axis is :

The number of common tangents, to the circles $x^{2}+y^{2}-18 x-15 y+131=0$ and $x^{2}+y^{2}-6 x-6 y-7=0$, is :

Choose the correct statement about two circles whose equations are given below :x2 + y2 $-$ 10x $-$ 10y + 41 = 0x2 + y2 $-$ 22x $-$ 10y +…

Let S1 : x2 + y2 = 9 and S2 : (x $-$ 2)2 + y2 = 1. Then the locus of center of a variable circle S which touches S1 internally and S2…

A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C1 : x2 + y2 + 2y $-$ 5 = 0 at two points P and Q such…

Let the abscissae of the two points P and Q be the roots of $2{x^2} - rx + p = 0$ and the ordinates of P and Q be the roots of ${x^2} - sx…