The line $L$ passes through the points of intersection of the circles ${x^2} + {y^2} = 25$ and ${x^2} + {y^2} - 8x + 7 = 0$. The length of perpendicular from centre of second circle onto the line $L$, is
$4$
$3$
$1$
$0$
The number of circles touching the line $y - x = 0$ and the $y$-axis is
The equation of the circle which passes through the point of intersection of circles ${x^2} + {y^2} - 8x - 2y + 7 = 0$ and ${x^2} + {y^2} - 4x + 10y + 8 = 0$ and having its centre on $y$ - axis, will be
Suppose $S_1$ and $S_2$ are two unequal circles, $A B$ and $C D$ are the direct common tangents to these circles. A transverse common tangent $P Q$ cuts $A B$ in $R$ and $C D$ in $S$. If $A B=10$, then $R S$ is
The equation of the circle which touches the circle ${x^2} + {y^2} - 6x + 6y + 17 = 0$ externally and to which the lines ${x^2} - 3xy - 3x + 9y = 0$ are normals, is
Circles ${x^2} + {y^2} - 2x - 4y = 0$ and ${x^2} + {y^2} - 8y - 4 = 0$