Find the equation of the normal to the circle $x^2 + y^2 - 5x + 2y - 48 = 0$ at the point $(5, 6)$.

If the line $lx + my + n = 0$ is a tangent to the circle $(x - h)^2 + (y - k)^2 = a^2$,then

Let the lines $(2-i)z = (2+i)\bar{z}$ and $(2+i)z + (i-2)\bar{z} - 4i = 0$ (where $i^2 = -1$) be normal to a circle $C$. If the line $iz + \bar{z} + 1 + i = 0$ is tangent to this circle $C$,then its radius is

If $y=\sqrt{3}x+k_1$ and $y=\sqrt{3}x+k_2$ are two parallel tangents of a circle of radius $2 \text{ units}$,then $|k_1-k_2|$ is equal to

If $O$ is the origin and $OP$,$OQ$ are tangents to the circle $x^2 + y^2 + 2gx + 2fy + c = 0$,the circumcentre of the triangle $OPQ$ is

The equations of the tangents to the circle $x^2+y^2=36$ which are perpendicular to the line $5x+y-2=0$ are