Let the equation of a circle be $x^{2}+y^{2}-6x-4y+9=0$. Then the line $4x+3y-8=0$ is a

If the length of the tangent drawn from the point $(5, 3)$ to the circle $x^2 + y^2 + ky + 17 = 0$ is $7$,then $k = \dots$

The tangent to the circle $C_1 : x^2 + y^2 - 2x - 1 = 0$ at the point $(2, 1)$ cuts off a chord of length $4$ from a circle $C_2$ whose centre is $(3, -2)$. The radius of $C_2$ is

The combined equation of the tangent and normal to the curve $xy = 100$ at the point $(5, 20)$ 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 angle between the tangents to the circle $x^2+y^2=25$ from the point $(1,7)$ is