Chapter 11.1, Problem 45E

To determine

To find: the equation of the parabola.

Answer to Problem 45E

The equation of parabola is $y^2=-3x$ .

Explanation of Solution

The equation of parabola is $y^2=-3x$ .

Given information:

From the given figure it can be observed that

Focal diameter = $\frac{3}{2}+\frac{3}{2}$

The graph of the parabola opens to the left.

The focus of graph is on the negative x-axis.

Calculation:because it is given that focus is on the negativex-axis, so the parabola should be with horizontal axis and $p<0$ .

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

  $y^2-4px$

Focal diameter of parabola = $\left|4p\right|$

Since focal diameter of parabola = $\frac{3}{2}+\frac{3}{2}$

So,

  $\begin{array}{l}\left|4p\right|=\frac{3}{2}+\frac{3}{2}\\ \left|4p\right|=3\text{ [add]}\\ -\left(4p\right)=3\text{ [remove the mod, because p<0 so it remove with negative sign]}\\ p=-\frac{3}{4}\text{ [divide by -4]}\end{array}$

So the equation of parabola is,

  $\begin{array}{l}{y}^2-4px\\ y^2-4\left(-\frac{3}{4}\right)x\text{ [substitute p by -}\frac{3}{4}\text{]}\\ y^2+3x\text{ [multiply and divide]}\\ y^2+3x=0\text{ [simplify]}\\ y^2=-3x\end{array}$

Hence, the equation of parabola is $y^2=-3x$ .