Chapter 11.1, Problem 48E

To determine

To find: the equation of the parabola.

Answer to Problem 48E

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

Explanation of Solution

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

Given information:

From the given figure it can be observed that,

The graph of the parabola opens to the right and parabola has horizontal axis.

The square made by directrix and parabola curve area is $16$ .

Calculation:here, the graph of parabola opens to the right so $p>0$ .

Because the parabola has horizonal axis,

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

  $y^2-4px$

Area of square area = $16$

Let $a$ be the side of the square.

Area of square = $a^2$

So,

  $\begin{array}{l}{a}^2=16\\ a=4\text{ [sqaure root]}\end{array}$

So the directrix should intercept the negative x-axis at $4$ .

Then the equation of directrix should be $x=-4$ .

The equation of directrix for parabola with horizontal axis $x=-p$

So, $p=4$

So the equation of parabola is,

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

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