Chapter 11.1, Problem 43E

To determine

To find: the equation of the parabola.

Answer to Problem 43E

The equation of parabola is $y^2=-16x$ .

Explanation of Solution

The equation of parabola is $y^2=-16x$ .

Given information:

From the figure provided in the question it can be observed that

Directrix $x=4$

The graph of parabola opens to the left.

Calculation: from the given directrix it can be observed that the parabola has horizontal axis.

So the equation of parabola should be in the following form,

  $y^2-4px$

For parabola with horizontal axis, directrix is $x=-p$ .

To comparing the directrix it can be observed that,

  $p=-4$

So the equation of parabola is,

  $\begin{array}{l}{y}^2-4px\\ y^2-4\left(-4\right)x\text{ [substitute p by -4]}\\ y^2+16x\text{ [multiply]}\\ y^2+16x=0\text{ [simplify]}\\ y^2=-16x\end{array}$

Hence, the equation of parabola is $y^2=-16x$ .