If the midpoint of a chord is $(-1, 1)$,find the equation of the chord of the parabola $y^2 = 6x$.

Tangents are drawn at three points $P(t_1), Q(t_2), R(t_3)$ on the parabola $y^2 = x$. Let these tangents intersect each other at the points $L, M, N$. If $t_1 = 2, t_2 = -4, t_3 = 6$,then the area of the triangle $LMN$ is

What is the distance between the focus and the directrix of the parabola $x^2 = -8y$?

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:

The angle between the two curves $y^2 = 4(x + 1)$ and $x^2 = 4(y + 1)$ is .............. $^\circ$.

An equilateral triangle is inscribed in the parabola $y^{2}=4ax$,where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.