If $(0, 0)$ is the vertex and $3x - 4y + 2 = 0$ is the directrix of a parabola,find the length of its latus rectum. (in $/5$)

If the three normals drawn to the parabola $y^{2} = 2x$ pass through the point $(a, 0)$ where $a \neq 0$,then $a$ must be greater than:

The normal at the point $(bt_1^2, 2bt_1)$ on the parabola $y^2 = 4bx$ meets the parabola again at the point $(bt_2^2, 2bt_2)$. Then:

If the tangents at the endpoints $P$ and $Q$ of a chord of a parabola meet at point $T$,then the distances of points $P, T, Q$ from the focus of the parabola are in which progression?

Find the equation of the parabola with focus $(0, -3)$ and directrix $y = 3$.

How many parabolas can be drawn if the two endpoints of the latus rectum are given?