Question

which is the directrix of a parabola with equation $x^{2}=8y$?
$y = 2$
$x=-2$
$y=-2$
$x = 2$

Explanation:

Step1: Recall parabola standard - form

The standard form of a parabola opening upwards or downwards is $x^{2}=4py$. Given $x^{2}=8y$, we can equate $4p = 8$.

Step2: Solve for $p$

Dividing both sides of $4p = 8$ by 4, we get $p=\frac{8}{4}=2$.

Step3: Find the directrix

For a parabola of the form $x^{2}=4py$ opening upwards, the directrix is given by the equation $y=-p$. Since $p = 2$, the directrix is $y=-2$.

Answer:

$y = - 2$