The point of intersection of the normals to the parabola $y^2 = 4x$ at the ends of its latus rectum is

The minimum distance between the parabola $y^2 = 8x$ and its image with respect to the line $x + y + 4 = 0$ is:

If tangents are drawn from the point $(-1, 2)$ to the parabola $y^2 = 4x$, what is the area of the triangle formed by the chord of contact and the tangents (in $\sqrt{2}$)?

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:

If the line $y = 2x + k$ is a normal to the parabola $y^2 = 4x$ at the point $(t^2, 2t)$,then:

Let the locus of the mid-point of the chord through the origin $O$ of the parabola $y^{2}=4x$ be the curve $S$. Let $P$ be any point on $S$. Then the locus of the point,which internally divides $OP$ in the ratio $3:1$,is: