Chapter 11.1, Problem 36E

To determine

To find: the equation of the parabola.

Answer to Problem 36E

The equation of parabola is $y^2=\frac{1}{2}x$ .

Explanation of Solution

The equation of parabola is $y^2=\frac{1}{2}x$ .

Given information:

Vertex $\left(0,0\right)$

Directrix $x=-\frac{1}{8}$

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,

  $p=\frac{1}{8}$

So the equation of parabola is,

  $\begin{array}{l}{y}^2-4px\\ y^2-4\left(\frac{1}{8}\right)x\text{ [substitute p by }\frac{1}{8}\text{]}\\ y^2-\frac{1}{2}x\text{ [multiply]}\\ y^2-\frac{1}{2}x=0\text{ [simplify]}\\ y^2=\frac{1}{2}x\end{array}$

Hence, the equation of parabola is $y^2=\frac{1}{2}x$ .