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

The slope of the chord of the parabola $y^2 = 4ax$ which passes through the origin and is normal at one of its endpoints is:

The locus of the point of intersection of the perpendicular tangents to the curve $y^2 + 4y - 6x - 2 = 0$ is:

What is the locus of the vertices $(x, y)$ of the parabolas $y = \frac{a^3x^2}{3} + \frac{a^2x}{2} - 2a$?

If $y = 2x - 3$ is a tangent to the parabola $y^2 = 4a(x - \frac{1}{3})$,then $a$ is equal to:

Let $P(4, 4\sqrt{3})$ be a point on the parabola $y^2 = 4ax$ and $PQ$ be a focal chord of the parabola. If $M$ and $N$ are the feet of the perpendiculars drawn from $P$ and $Q$ respectively on the directrix of the parabola,then the area of the quadrilateral $PQMN$ is equal to: