The radius of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ and having its centre at $(0,3)$ is

If $\lambda$ is the perpendicular distance of a point $P$ on the circle $x^2+y^2+2x+2y-3=0$ from the line $2x+y+13=0$,then the maximum possible value of $\lambda$ is

The centre of the smallest circle touching the circles $x^2 + y^2 - 2y - 3 = 0$ and $x^2 + y^2 - 8x - 18y + 93 = 0$ is:

If $\sin ^{-1} a$ is the acute angle between the curves $x^{2}+y^{2}=4 x$ and $x^{2}+y^{2}=8$ at $(2,2)$,then $a$ is equal to

Let $PQ$ and $RS$ be tangents at the endpoints of the diameter $PR$ of a circle of radius $r$. If $PS$ and $RQ$ intersect at a point $X$ on the circumference of the circle,then the length of the chord through $X$ perpendicular to the diameter $PR$ is:

Consider the circle $x^2+y^2-4x-2y+c=0$ whose centre is $A(2,1)$. If the point $P(10,7)$ is such that the line segment $PA$ meets the circle in $Q$ with $PQ=5$,then $c$ is equal to