Find the parameter $t$ for the point $(4, -6)$ on the parabola $y^2 = 9x$.

Find the equation of the parabola whose focus is $(-1, -2)$ and whose directrix is the line $x - 2y + 3 = 0$.

Let one root of the quadratic equation in $x$: $(k^2 - 15k + 27)x^2 + 9(k-1)x + 18 = 0$ be twice the other. Then the length of the latus rectum of the parabola $y^2 = 6kx$ is equal to:

The equation of the normal to the parabola $y^2 = 4ax$ at the point $\left( \frac{a}{m^2}, \frac{2a}{m} \right)$ is:

The axis of a parabola lies along the $x$-axis. If its vertex and focus are at distances $2$ and $4$ respectively from the origin on the positive $x$-axis,then which of the following points does not lie on it?

$A$ point on the parabola whose axis is parallel to the $X$-axis and which passes through the points $(0,1), (3,0), (0,-2)$ is