Question

If a parabola passing through point $(-4,-2)$ has its vertex at the origin and $y-$axis as its axis of symmetry, then the length of the latus rectum of the parabola is

Answer 1

Since the parabola has its vertex at the origin and $y-$axis as its axis of symmetry and also passes through point $(-4,-2)$,
so, the equation of parabola will be in the form $x^2=-4ay$
Since parabola passes through point $(-4,-2),$
$\therefore (-4{)}^2=-4a(-2)$
$\Rightarrow a=2$
Length of the latus rectum $=4a=8$