The straight line touching the circle $x^2+y^2-2x-3=0$ and remaining normal to the circle $x^2+y^2-4y-6=0$ is

If the shortest distance between the parabola $y^2=4x$ and the circle $x^2+y^2-4x-16y+64=0$ is $d$,then $d^2$ is equal to:

Let $AB$ be a chord of the circle $x^2 + y^2 = r^2$ subtending a right angle at the centre. Then the locus of the centroid of the $\Delta PAB$ as $P$ moves on the circle is

If $y = m_{1}x + c_{1}$ and $y = m_{2}x + c_{2}$ with $m_{1} \neq m_{2}$ are two common tangents of the circle $x^{2} + y^{2} = 2$ and the parabola $y^{2} = x$,then the value of $8|m_{1}m_{2}|$ is equal to

$ax - y + c = 0$ is the equation of the common tangent to the parabola $y^2 = 8\sqrt{5}x$ and the circle $x^2 + y^2 = 1$. If this tangent makes an acute angle with the positive $X$-axis,then $a^2c^2 =$

For the circle $C$ with the equation $x^2+y^2-16x-12y+64=0$,match the List-$I$ with the List-$II$ given below.

List-$I$	List-$II$
$(i)$ The equation of the polar of $(-5, 1)$ with respect to $C$	$(A)$ $y = 0$
$(ii)$ The equation of the tangent at $(8, 0)$ to $C$	$(B)$ $y = 6$
$(iii)$ The equation of the normal at $(2, 6)$ to $C$	$(C)$ $x + y = 7$
$(iv)$ The equation of the diameter of $C$ through $(8, 12)$	$(D)$ $13x + 5y = 98$
	$(E)$ $x = 8$

The correct match is: