Chapter 6.7, Problem 47E

To determine

To identify : The focus directrix, and axis of symmetry of the parabola and then graph the equation.

Answer to Problem 47E

The focus is $\left(0.1,0\right)$ , the directrix is $x=-0.1$ and the axis of symmetry is x axis.

Explanation of Solution

Given information :

The given parabola is $y^2=\frac{2}{5}x$

Calculation :

The given equation can be written as

  $\begin{array}{l}x=\frac{5}{2}{y}^2\\ x=\frac{1}{4\cdot \frac{1}{10}}{y}^2\end{array}$

The equation has the form $x=\frac{1}{4p}{y}^2$ , where $p=\frac{1}{10}=0.1$ . Therefore,

The focus is $\left(p,0\right)$ or $\left(0.1,0\right)$ .

The directrix is $x=-p$ or $x=-0.1$ . Because y is squared so the axis of symmetry is x axis.

The graph of the parabola is drawn below:

  

Hence,

The focus is $\left(0.1,0\right)$ , the directrix is $x=-0.1$ and the axis of symmetry is x axis.