The equations of the common tangents to the ellipse $x^2 + 4y^2 = 8$ and the parabola $y^2 = 4x$ are

Match the conics in Column-$I$ with the statements/expressions in Column-$II$.

Column-$I$	Column-$II$
$A$. Circle	$P$. Locus of point $(h, k)$ such that the line $hx + ky = 1$ touches the circle $x^2 + y^2 = 4$
$B$. Parabola	$Q$. Point $z$ in the complex plane satisfies $|z + 2| - |z - 2| = \pm 3$
$C$. Hyperbola	$R$. Eccentricity of the conic lies in the interval $[1, \infty)$
	$S$. Point $z$ in the complex plane satisfies $Re(z + 1)^2 = |z|^2 + 1$

Consider the circle $x^2+y^2=9$ and the parabola $y^2=8x$. They intersect at $P$ and $Q$ in the first and the fourth quadrants,respectively. Tangents to the circle at $P$ and $Q$ intersect the $x$-axis at $R$ and tangents to the parabola at $P$ and $Q$ intersect the $x$-axis at $S$.
$1.$ The ratio of the areas of the triangles $PQS$ and $PQR$ is
$(A)$ $1:\sqrt{2}$ $(B)$ $1:2$ $(C)$ $1:4$ $(D)$ $1:8$
$2.$ The radius of the circumcircle of the triangle $PRS$ is
$(A)$ $5$ $(B)$ $3\sqrt{3}$ $(C)$ $3\sqrt{2}$ $(D)$ $2\sqrt{3}$
$3.$ The radius of the incircle of the triangle $PQR$ is
$(A)$ $4$ $(B)$ $3$ $(C)$ $8/3$ $(D)$ $2$
Give the answer for questions $1, 2$ and $3.$

If the curves $y^2=16x$ and $9x^2+\alpha y^2=25$ intersect at right angles,then $\alpha=$

If a normal to a parabola $y^2 = 4ax$ makes an angle $\phi$ with its axis,then it will cut the curve again at an angle

The normal at $\left( 2, \frac{3}{2} \right)$ to the ellipse $\frac{x^2}{16} + \frac{y^2}{3} = 1$ touches a parabola,whose equation is