Question

which is the directrix of a parabola with equation $x^{2}=4y$?
$y = 1$
$x=-1$
$y=-1$
$x = 1$

Explanation:

Step1: Recall the standard - form of parabola equation

The standard form of a parabola opening upwards or downwards is $x^{2}=4py$. Comparing $x^{2}=4y$ with $x^{2}=4py$, we get $4p = 4$.

Step2: Solve for $p$

Dividing both sides of $4p = 4$ by 4, we have $p=\frac{4}{4}=1$.

Step3: Find the directrix

For a parabola of the form $x^{2}=4py$ opening upwards (since $p = 1>0$), the equation of the directrix is $y=-p$. Substituting $p = 1$ into $y=-p$, we get $y=-1$.

Answer:

$y = - 1$