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 :
$3$
$2$
$1$
$4$
The distance from the centre of the circle $x^2 + y^2 = 2x$ to the straight line passing through the points of intersection of the two circles $x^2 + y^2 + 5x -8y + 1 =0$ and $x^2 + y^2-3x + 7y -25 = 0$ is-
The equation of the image of the circle ${x^2} + {y^2} + 16x - 24y + 183 = 0$ by the line mirror $4x + 7y + 13 = 0$ is
Two tangents are drawn from a point $P$ on radical axis to the two circles touching at $Q$ and $R$ respectively then triangle formed by joining $PQR$ is
The number of common tangents to the circles ${x^2} + {y^2} - x = 0,\,{x^2} + {y^2} + x = 0$ is
The number of circles touching the line $y - x = 0$ and the $y$-axis is