The normal drawn at $(1,1)$ to the circle $x^2+y^2-4x+6y-4=0$ is

The equation of the normal to the circle $x^2 + y^2 = 9$ at the point $\left( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right)$ is

If a line passing through the origin touches the circle $(x - 4)^2 + (y + 5)^2 = 25$,then its slope is:

If $m_1, m_2$ are the slopes of the tangents drawn through the point $(-1, -2)$ to the circle $(x-3)^2 + (y-4)^2 = 4$,then $\sqrt{3}|m_1 - m_2| = $

If $(3,-1)$ is one end of a diameter of the circle $x^2+y^2-2x+4y=0$,then the equation of the tangent at the other end of that diameter is

Let $AB$ be a chord of length $12$ of the circle $(x-2)^{2}+(y+1)^{2}=\frac{169}{4}$. If tangents drawn to the circle at points $A$ and $B$ intersect at the point $P$,then five times the distance of point $P$ from chord $AB$ is equal to $.......$