If the point on the curve $y^{2}=6x$,nearest to the point $\left(3, \frac{3}{2}\right)$ is $(\alpha, \beta)$,then $2(\alpha+\beta)$ is equal to $.....$

If one end of a focal chord of the parabola $y^2 = 16x$ is $(1, -4)$,find the other end.

Let the curve $C$ be the mirror image of the parabola $y^2=4x$ with respect to the line $x+y+4=0$. If $A$ and $B$ are the points of intersection of $C$ with the line $y=-5$,then the distance between $A$ and $B$ is

What is the equation of the pair of tangents drawn from the point $(1, 4)$ to the parabola $y^2 = 12x$?

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

The vertex of a parabola is $(2, 2)$ and the coordinates of the two extremities of its latus rectum are $(-2, 0)$ and $(6, 0)$. The equation of the parabola is