The minimum distance between any two points $P _{1}$ and $P _{2}$ while considering point $P _{1}$ on one circle and point $P _{2}$ on the other circle for the given circles' equations
$x^{2}+y^{2}-10 x-10 y+41=0$
$x^{2}+y^{2}-24 x-10 y+160=0$ is .........
$4$
$3$
$2$
$1$
The locus of centre of a circle passing through $(a, b)$ and cuts orthogonally to circle ${x^2} + {y^2} = {p^2}$, is
If $y = 2x$ is a chord of the circle ${x^2} + {y^2} - 10x = 0$, then the equation of the circle of which this chord is a diameter, is
Consider a family of circles which are passing through the point $(- 1, 1)$ and are tangent to $x-$ axis. If $(h, k)$ are the coordinate of the centre of the circles, then the set of values of $k$ is given by the interval
The points of intersection of circles ${x^2} + {y^2} = 2ax$ and ${x^2} + {y^2} = 2by$ are