The two circles ${x^2} + {y^2} - 2x + 22y + 5 = 0$ and ${x^2} + {y^2} + 14x + 6y + k = 0$ intersect orthogonally provided $k$ is equal to
$47$
$ - 47$
$49$
$ - 49$
If the circles ${x^2} + {y^2} = {a^2}$and ${x^2} + {y^2} - 2gx + {g^2} - {b^2} = 0$ touch each other externally, then
A circle passes through the origin and has its centre on $y = x$. If it cuts ${x^2} + {y^2} - 4x - 6y + 10 = 0$ orthogonally, then the equation of the circle is
Choose the correct statement about two circles whose equations are given below
$x^{2}+y^{2}-10 x-10 y+41=0$
$x^{2}+y^{2}-22 x-10 y+137=0$
In the co-axial system of circle ${x^2} + {y^2} + 2gx + c = 0$, where $g$ is a parameter, if $c > 0$ then the circles are
Radius of circle touching $y-$axis at point $P(0,2)$ and circle $x^2 + y^2 = 16$ internally-