The equations of tangents to the circle ${x^2} + {y^2} - 22x - 4y + 25 = 0$ which are perpendicular to the line $5x + 12y + 8 = 0$ are
$12x - 5y + 8 = 0$, $12x - 5y = 252$
$12x - 5y = 0,\,\,12x - 5y = 252$
$12x - 5y - 8 = 0,\,12x - 5y + 252 = 0$
None of these
If ${c^2} > {a^2}(1 + {m^2}),$ then the line $y = mx + c$ will intersect the circle ${x^2} + {y^2} = {a^2}$
Let a circle $C$ of radius $5$ lie below the $x$-axis. The line $L_{1}=4 x+3 y-2$ passes through the centre $P$ of the circle $C$ and intersects the line $L _{2}: 3 x -4 y -11=0$ at $Q$. The line $L _{2}$ touches $C$ at the point $Q$. Then the distance of $P$ from the line $5 x-12 y+51=0$ is
Tangents are drawn from $(4, 4) $ to the circle $x^2 + y^2 - 2x - 2y - 7 = 0$ to meet the circle at $A$ and $B$. The length of the chord $AB $ is
Equation of a line through $(7, 4)$ and touching the circle, $x^2 + y^2 - 6x + 4y - 3 = 0$ is :
If a line passing through origin touches the circle ${(x - 4)^2} + {(y + 5)^2} = 25$, then its slope should be