The length of the tangent drawn from the point $(2, 3)$ to the circle $2(x^2 + y^2) - 7x + 9y - 11 = 0$ is:

If the coordinates of one end of a diameter of the circle $x^2+y^2+4x-8y+5=0$ are $(2,1)$, then the coordinates of the other end are:

In the figure shown,the radius of circle $C_1$ is $r$ and that of $C_2$ is $\frac{r}{2}$,where $r = \frac{1}{3} PQ$. Then the length of $AB$ is (where $P$ and $Q$ are the centers of $C_1$ and $C_2$ respectively).

$A$ circle passes through the point $(0, 1)$ and touches the parabola $y = x^2$ at the point $(1, 1)$. The centre of the circle is...

If $Q(h, k)$ is the inverse point of the point $P(1, 2)$ with respect to the circle $x^2+y^2-4x+1=0$,then $2h+k=$

If one of the diameters of the circle $x^{2}+y^{2}-2 \sqrt{2} x-6 \sqrt{2} y+14=0$ is a chord of the circle $(x-2 \sqrt{2})^{2}+(y-2 \sqrt{2})^{2}=r^{2}$,then the value of $r^{2}$ is equal to