Question

Please Help!!!! Find the equation of the directrix of the parabola: 1/12*x^2=y Please explain and show your work.

Answer 1

Hmmm  recall, p=3, and "p" is the distance from the vertex to either, the focus or directrix, so if the focus is 3 units to one-side of the vertex, the directrix is 3 units to the other side

check the picture below

Answer 2

Answer:

$y=-3$

Step-by-step explanation:

We have been an equation $y=\frac{1}{12}x^2$. We are asked to find the equation of directrix for our given parabola.

We know that standard form of parabola is in form $4p(y-k)=(x-h)^2$ with vertex at point $(h,k)$ and focal length of $|p|$.

Let us convert our given equation in standard form as:

$12*y=12*\frac{1}{12}x^2$

$12y=x^2$

$4\cdot 3y=x^2$

$4\cdot 3(y-0)=(x-0)^2$

The vertex of our given parabola is (0,0) and focal length is p.

The equation of directrix is in form $y=k-p$.

From our given equation, we can see that $h=0,k=0\text{ and }p=3$.

So the equation of directrix will be $y=0-3$

$y=-3$

Therefore, the equation of directrix is $y=-3$.