Question

Which is the directrix of parabola with equation x^2=4y

Answer 1

Answer:

$y=-1$

Step-by-step explanation:

We have been given an equation of parabola $x^2=4y$. We are asked to find the directrix of our given parabola.    

First of all, we will divide both sides of our given equation by 4.

$\frac{x^2}{4}=\frac{4y}{4}$      

$\frac{x^2}{4}=y$      

$y=\frac{x^2}{4}$      

Now, we will compare our equation with vertex form of parabola:

$y=a(x-h)^2+k$, where, (h,k) represents vertex of parabola.

We can see that the value of a is $\frac{1}{4}$, $h=0$ and $k=0$.

Now, we will find distance of focus from vertex of parabola using formula $p=\frac{1}{4a}$.

Substituting the value of a in above formula, we will get:

$p=\frac{1}{4*\frac{1}{4}}$

$p=\frac{1}{1}=1$

We know that directrix of parabola is $y=k-p$.

Substituting the value of k and p in above formula, we will get:

$y=0-1$

$y=-1$

Therefore, the directrix of our given parabola is $y=-1$.