The equations of the normals to the circle $x^2 + y^2 - 8x - 2y + 12 = 0$ at the points whose ordinate is $-1$ are:

The equation of the pair of tangents drawn from the point $(1, 1)$ to the circle $x^2 + y^2 + 2x + 2y + 1 = 0$ is:

If the slope of the tangent of the circle $S \equiv x^2+y^2-13=0$ at $(2,3)$ is $m$,then the point $\left(m, \frac{-1}{m}\right)$ is

If the line $ax+by=1$ is a tangent to the circle $S_r \equiv x^2+y^2-r^2=0$,then which one of the following is true?

The circle $x=5 \cos \theta, y=5 \sin \theta$ is bounded by the rectangle formed by the lines $x \pm 6=0$ and $y \pm 6=0$. The area of the triangle that lies inside the rectangle,which is formed by the tangent at $P\left(\frac{2 \pi}{3}\right)$ to the circle with two of the above given lines,is

The normal to the circle $x^2 + y^2 - 3x - 6y - 10 = 0$ at the point $(-3, 4)$ is