Question

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

Answer 1

`y=-1`

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.

`(x^2)/(4)=(4y)/(4)`

`(x^2)/(4)=y`

`y=(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
`(1)/(4)`,
`h=0` and
`k=0`.

Now, we will find distance of focus from vertex of parabola using formula
`p=(1)/(4a)`.

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

`p=(1)/(4*(1)/(4))`

`p=(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`.