A circle with radius $12$ lies in the first quadrant and touches both the axes, another circle has its centre at $(8,9)$ and radius $7$. Which of the following statements is true

If the two circles $2{x^2} + 2{y^2} - 3x + 6y + k = 0$ and ${x^2} + {y^2} - 4x + 10y + 16 = 0$ cut orthogonally, then the value of $k$ is

If the circles of same radius a and centers at $(2, 3)$ and $(5, 6)$ cut orthogonally, then $a =$

The two circles ${x^2} + {y^2} - 4y = 0$ and ${x^2} + {y^2} - 8y = 0$

The locus of centre of a circle passing through $(a, b)$ and cuts orthogonally to circle ${x^2} + {y^2} = {p^2}$, is

Choose the correct statement about two circles whose equations are given below

$x^{2}+y^{2}-10 x-10 y+41=0$

$x^{2}+y^{2}-22 x-10 y+137=0$