The locus of the mid-point of the line segment joining the focus and any point on the parabola $y^{2}=4ax$ is a parabola. Find the equation of its directrix.

The equation of the parabola whose focus is $(5, 3)$ and directrix is $3x - 4y + 1 = 0$ is:

Statement $(A)$: If the normal at the ends of the latus rectum of the parabola $y^2 = 4x$ meet the curve again at $P$ and $P'$,then $PP' = 12$ units.
Reason $(R)$: If the normal at $T_1$ to the parabola $y^2 = 4ax$ meets the parabola again at $T_2$,then $T_2 = -T_1 - \frac{2}{T_1}$.

If the tangent to the parabola $4y^2 = x$ makes an angle of $60^{\circ}$ with the $x$-axis,then find its point of contact.

Study the following statements.
$I$. The vertex of the parabola $x = ly^2 + my + n$ is $\left(n - \frac{m^2}{4l}, -\frac{m}{2l}\right)$.
$II$. The focus of the parabola $y = lx^2 + mx + n$ is $\left(-\frac{m}{2l}, n - \frac{m^2-1}{4l}\right)$.
$III$. The pole of the line $lx + my + n = 0$ with respect to the parabola $x^2 = 4ay$ is $\left(-\frac{2al}{m}, \frac{n}{m}\right)$.
Then,the correct option among the following is:

If $(2,3)$ is the vertex and $(3,2)$ is the focus of a parabola,then its equation is