Chapter 9.3, Problem 4WE

To determine

To find: The directrix of the parabola.

Answer to Problem 4WE

The directrix is $x=5$ .

Explanation of Solution

Given information: It is given that $V\left(1,-1\right)$ and $F\left(-3,-1\right)$ .

Formula used: For parabola:

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

Calculation: Since $V\left(1,-1\right)$

  $\begin{array}{l}\therefore \left(h,k\right)=\left(1,-1\right)\\ \therefore h=1\&k=-1\end{array}$

Similarly, $F\left(-3,-1\right)$

  $\begin{array}{l}\because \left(h+c,k\right)=\left(-3,-1\right)\\ \therefore -1+c=-3\left[\because k=-1\right]\\ c=-4\end{array}$

Now, the directrix is:

  $\begin{array}{l}x=h-c\\ x=1-\left(-4\right)\\ x=5\end{array}$

Therefore, the required directrix is $x=5$ .