The equation of the tangent to the curve given by $x=3 \cos \theta, y=3 \sin \theta$ at $\theta=\frac{\pi}{4}$ is

The equations of the tangents to the circle $x^{2}+y^{2}=13$ at the points whose abscissa is $2$ are:

The length of the tangent from a point $P(x_1, y_1)$ to the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ is given by:

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

Match the points on the curve $2y^2 = x + 1$ with the slopes of the normals at those points and choose the correct answer.

$A. (7, 2)$	$1. -4\sqrt{2}$
$B. (0, 1/\sqrt{2})$	$2. -8$
$C. (1, -1)$	$3. 4$
$D. (3, \sqrt{2})$	$4. 0$
	$5. -2\sqrt{2}$

The tangent to the circle $x^2 + y^2 = 5$ at the point $(1, -2)$ also touches the circle $x^2 + y^2 - 8x + 6y + 20 = 0$. Find its point of contact.