The length of the latus rectum of the parabola $y^2+8x-2y+17=0$ is

If a double ordinate of the parabola $y^2 = 4ax$ has a length of $8a$,then the angle between the lines joining the vertex of the parabola to the ends of this double ordinate is ............... $^\circ$.

What is the equation of the normal to the curve $y^2 = 16x$ at the point $(1, 4)$?

For the parabola $y^2+6y-2x+5=0$,match the items in List-$I$ with the suitable item in List-$II$ given below:

List-$I$ (Geometric Property)	List-$II$ (Coordinates/Equations)
$I$. Vertex	$A$. $\left(-\frac{3}{2}, -3\right)$
$II$. Focus	$B$. $\left(\frac{3}{2}, -3\right)$
$III$. Equation of the directrix	$C$. $2x + 5 = 0$
$IV$. Equation of the axis	$D$. $2x + y + 3 = 0$
	$E$. $y + 3 = 0$
	$F$. $(-2, -3)$

The correct matching is:

If the line $x + my + am^2 = 0$ is tangent to the parabola $y^2 = 4ax$,find the point of contact.

The slope of the line touching both the parabolas $y^2 = 4x$ and $x^2 = -32y$ is