Chapter 9.3, Problem 1OE

To determine

To find: The directrix.

Answer to Problem 1OE

The directrix is $x=3$ .

Explanation of Solution

Given information: It is given that $V\left(0,0\right)$ and $F\left(-3,0\right)$ .

Formula used: For parabola: $y-k=\frac{1}{4c}{\left(x-h\right)}^2$ :

  $\begin{array}{l}Vertex\left(h,k\right)\\ Focus\left(h+c,k\right)\\ D:y=h-c\end{array}$

Calculation: Since $V\left(0,0\right)$

  $\therefore \left(h,k\right)=\left(0,0\right)$

Similarly, $F\left(-3,0\right)$

  $\begin{array}{l}\because \left(h+c,k\right)=\left(-3,0\right)\\ \therefore c=-3\end{array}$

Now, the directrix is:

  $\begin{array}{l}x=h-c\\ x=0-\left(-3\right)\\ x=3\end{array}$

Therefore, the required directrix is $x=3$ .