If the line $3x - 4y - k = 0 (k > 0)$ touches the circle $x^2 + y^2 - 4x - 8y - 5 = 0$ at $(a, b)$,then $k + a + b$ is equal to:

The equations of the tangents to the circle $x^2 + y^2 = 4$,which are parallel to $x + 2y + 3 = 0$,are

Let the lines $y+2x=\sqrt{11}+7\sqrt{7}$ and $2y+x=2\sqrt{11}+6\sqrt{7}$ be normal to a circle $C:(x-h)^{2}+(y-k)^{2}=r^{2}$. If the line $\sqrt{11}y-3x=\frac{5\sqrt{77}}{3}+11$ is tangent to the circle $C$,then the value of $(5h-8k)^{2}+5r^{2}$ is equal to.......

Let $O$ be the origin and $OP$ and $OQ$ be the tangents to the circle $x^2+y^2-6x+4y+8=0$ at the points $P$ and $Q$ on it. If the circumcircle of the triangle $OPQ$ passes through the point $(\alpha, \frac{1}{2})$,then a value of $\alpha$ is

The value of $c$,for which the line $y = 2x + c$ is a tangent to the circle $x^2 + y^2 = 16$,is

The normal drawn at $P(-1, 2)$ on the circle $x^2+y^2-2x-2y-3=0$ meets the circle at another point $Q$. Then,the coordinates of $Q$ are