Find the length of the latus rectum of a parabola if $PSQ$ is a focal chord such that $SP = 3$ and $SQ = 2$.

What is the vertex of the parabola $x^2 + 4x + 2y - 7 = 0$?

Two tangents are drawn from the point $(-1, -2)$ to the parabola $y^2 = 4x$. If $\theta$ is the angle between these tangents,then $\tan \theta = $

What are the parametric equations of the parabola $y^2 = 8x$?

The point of intersection of the latus rectum and the axis of the parabola ${y^2} + 4x + 2y - 8 = 0$ is:

The maximum area of a circle centered at the origin,which is inscribed in the parabola $y = x^2 - 100$,can be expressed as $\frac{a\pi}{b}$,where $a$ and $b$ are coprime numbers. Then the value of $a + b$ is: