Question

Label the focus, directrix, and vertex on the graphs given for

the parabolas in Exercises 2 and 3.

(a) $x^2=12y$

(b) $y^2=12x$

Short answer

a. The vertex, focus and directrix of the parabola $x^2=12y$labelled on the graph is , as follows:

b. The vertex, focus and directrix of the parabola $y^2=12x$labelled on the graph is , as follows:

Step-by-step solution

a.Step 1. Given information.

The given equation of a parabola $x^2=12y$.

Step 2. Write the concept.

The given equation of a parabola $x^2=12y$

Putting the equation in standard form $x^2=4ay$

Thus we get, a = 3

$\therefore$ the focus is $\left(0,3\right)$, the directrix is $y=-3$ and vertex is (0,0)

b.Step 1. Given information.

The given equation of a parabola $y^2=12x$.

Step 2. Write the concept.

The given equation of a parabola $y^2=12x$

Putting the equation in standard form $y^2=4ax$

Thus we get, a = 3

$\therefore$ the focus is $\left(3,0\right)$, the directrix is $x=-3$ and vertex is (0,0)