Chapter 11.1, Problem 76E

To determine

To find the coordinates of the focus and the equation of the directrix of given parabola and graph the equation.

Explanation of Solution

Given:

The equation of parabola is -

  $y^2=12x$

Calculation:

Comparing the above equation with the standard equation of parabola as follows-

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

Here

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

Therefore, the coordinates of focus are $(h+p,k)=(3,0)$

And the equation of directrix is $x=h-p\Rightarrow x=-3$

The following is the graph of the parabola