Find the equation of the parabola which is symmetric about the $y$-axis and passes through the point $(2, -3)$.

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} = $

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 $.....$

The locus of the mid-point of the line segment joining the focus of the parabola $y^{2}=4ax$ to a moving point of the parabola,is another parabola whose directrix is

$y = 3x - 2$ is a straight line touching the parabola $(y - 3)^2 = 12(x - 2)$. If a line drawn perpendicular to this line at point $P$ on it touches the given parabola,then the point $P$ is:

Find the equation of the tangent to the curve $y^2 = 6x$ at the point $(2, -3)$.