If the equation of a system of parallel chords of the parabola $y^2 = \frac{2}{3}x$ is $y + 2x + 1 = 0$,find its diameter.

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

If ${y_1}$ and ${y_2}$ are the ordinates of two points $P$ and $Q$ on the parabola ${y^2 = 4ax}$ and ${y_3}$ is the ordinate of the point of intersection of the tangents at $P$ and $Q$,then:

If the focus of a parabola divides a focal chord of the parabola into segments of lengths $5$ and $3$ units,then the length of the latus rectum of that parabola is:

The length of the latus rectum of the parabola $y^2+8x-2y+17=0$ is

The tangents drawn at the endpoints of the latus rectum of a parabola $S = 0$ intersect on the line $x + y = 2$. If $(3, 2)$ is the focus of the parabola,then the axis of the parabola $S = 0$ is: