Chapter A5.1, Problem 7E

To determine

To find: the given parabolas focus and directrix.

Answer to Problem 7E

The given parabolas focus is $(p,0)=(2,0)$ and directrix $x=-2$ .

Explanation of Solution

Given:

  $y^2=8x$

Calculation:

The given parabolas focus and directrixis calculated below

  $y^2=8x$

We find the value of p in the standard equation

  $\begin{array}{l}{y}^2=4px\\ 4p=8\\ p=2\end{array}$

focus : $(p,0)=(2,0)$

directrix : $x=-p\text{ or }x=-2$

Conclusion:

Therefore, thegiven parabolas focus is $(p,0)=(2,0)$ and directrix $x=-2$ .