Let $P$ represent the point $(3, 6)$ on the parabola $y^2 = 12x$. For the parabola $y^2 = 12x$,if $l_1$ is the length of the normal chord drawn at $P$ and $l_2$ is the length of the focal chord drawn through $P$,then $\frac{l_1}{l_2} = $

The axis of the parabola $x^{2}+2 x y+y^{2}-5 x+5 y-5=0$ is

Let $O$ be the vertex and $Q$ be any point on the parabola $x^2=8y$. If the point $P$ divides the line segment $OQ$ internally in the ratio $1:3$, then the locus of $P$ is

The coordinates of a point on the parabola $y^2 = 8x$ whose focal distance is $4$ are:

If $P$ and the origin are the points of intersection of the parabolas $y^2=32x$ and $2x^2=27y$,and if $\theta$ is the acute angle between these curves at $P$,then $5\sqrt{\tan \theta} =$

Assertion $(A)$: The curves $y^2 = 4x$ and $x^2 = -2y$ intersect at $(0,0)$ and $(2, -2)$ orthogonally.
Reason $(R)$: If the product of the slopes of the tangents drawn to two curves at their point of intersection is $-1$,then the curves are said to cut each other orthogonally. The correct option among the following is: