Chapter A5.1, Problem 15E

To determine

To find: focus and directrix and sketch the parabola.

Answer to Problem 15E

The parabola’s focus and directrix is:

Focus: $\left(p,0\right)=\left(3,0\right)$

Directrix: $x=-p$ or $x=-3$

The sketch of the parabola is:

  

Explanation of Solution

Given:

  $y^2=12x$

Calculation:

The given equation is-

  $y^2=12x$

Find the value of $p$ in the standard equation $y^2=4px:$

  $\begin{array}{l}4p=12\\ \Rightarrow p=3\end{array}$

Then find the focus and directrix for the value of $p$ :

Focus: $\left(p,0\right)=\left(3,0\right)$

Directrix: $x=-p$ or $x=-3$

Following is the sketch of the parabola:

  

Conclusion:

The parabola’s focus and directrix is:

Focus: $\left(p,0\right)=\left(3,0\right)$

Directrix: $x=-p$ or $x=-3$

The sketch of the parabola is: