The locus of the points of intersection of perpendicular normals to the parabola $y^2=4ax$ is

The angle between the tangents drawn from the origin to the parabola $y^2 = 4a(x - a)$ is ............... $^\circ$.

If $b$ and $c$ are the lengths of the segments of any focal chord of the parabola $y^2 = 4ax$,then what is the length of the semi-latus rectum?

$A$ normal with slope $\frac{1}{\sqrt{6}}$ is drawn from the point $(0, -\alpha)$ to the parabola $x^2 = -4ay$,where $a > 0$. Let $L$ be the line passing through $(0, -\alpha)$ and parallel to the directrix of the parabola. Suppose that $L$ intersects the parabola at two points $A$ and $B$. Let $r$ denote the length of the latus rectum and $s$ denote the square of the length of the line segment $AB$. If $r : s = 1 : 16$,then the value of $24a$ is. . . .

If the vertex of the conic $y^{2}-4y=4x-4a$ always lies between the straight lines $x+y=3$ and $2x+2y-1=0$, then:

If the normal to the parabola $y^2 = 4ax$ at the point with parameter $t_1$ cuts the parabola again at the point with parameter $t_2$,then: