Chapter 8.1, Problem 11E

Solution

To find: An equation in standard form for the parabola that satisfies the given conditions.

The required equation is $y^2=-12x$ .

Given: Vertex $=\left(0,0\right)$ , focus $=\left(-3,0\right)$

Concept used:

For Vertex: $\left(h,k\right)$ and Focus: $\left(\begin{array}{l}h+p,k\\ \end{array}\right)$

The standard equation: ${\left(y-k\right)}^2=4p\left(x-h\right)$

Calculation:

The axis of the parabola is the line passing through vertex $\left(0,0\right)$ and focus $\left(-3,0\right)$ .

And its equation is $y=0$ .

The directed distance from the vertex to focus is $p=-3-0$ .That is $p=-3$ .

Thus, $4p=-12$ .

So, the required equation will be

  $\begin{array}{c}{\left(y-0\right)}^2=-12\left(x-0\right)\\ y^2=-12x\end{array}$