Find the axis, vertex, focus, equation of directrix, latus rectum and length of the latus rectum for the parabola $y^2 = -8 x$. Also sketch its graph.
Given equation of parabola is: $\;\;$ $y^2 = -8x$
i.e.$\left(y - 0\right)^2 = - 4 \times 2 \times \left(x - 0\right)$ $\;\;\; \cdots \; (1)$
Comparing equation $(1)$ with the standard equation: $\;$ $\left(y - k\right)^2 = - 4 a \left(x - h\right)$ $\;$ gives
$\left(h , k\right) = \left(0,0\right)$; $\;\;$ $a = 2$
$\therefore$ $\;$ For the given parabola,
