Chapter 11.1, Problem 47E

To determine

To find: the equation of the parabola.

Answer to Problem 47E

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

Explanation of Solution

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

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.

Point on parabola $\left(4,-2\right)$ .

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,

  $y^2-4px$

Point on parabola is $\left(4,-2\right)$ , so it satisfy the equation of parabola.

Substitute $x=4\text{ and }y=-2$ in the equation,

  $\begin{array}{l}{y}^2-4px=0\\ {\left(-2\right)}^2-4p\left(4\right)=0\text{ [substitute }x\text{ by 4 and }y\text{ by -2]}\\ 4-16p=0\text{ [simplify]}\\ 16p=4\text{ [add }16p]\\ p=\frac{4}{16}\text{ [divide by 16]}\\ p=\frac{1}{4}\text{ [simplify]}\end{array}$

So the equation of parabola is,

  $\begin{array}{l}{y}^2-4px\\ y^2-4\left(\frac{1}{4}\right)x\text{ [substitute p by }\frac{1}{4}\text{]}\\ y^2-x\text{ [multiply and divide]}\\ y^2-x=0\text{ [simplify]}\\ y^2=x\end{array}$

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