Chapter 2, Problem 10CR

To determine

To find: The focus, directrix and axis of symmetry of the equation $36y=x^2$ .

Answer to Problem 10CR

Focus of the given equation $36y=x^2$ is $(0,9)$ .

Directrix of the given equation $36y=x^2$ is $y=-9$ .

The axis of symmetry is $x=0$ or the $y-$ axis.

  

Explanation of Solution

Given information: $36y=x^2$ .

From the given equation $36y=x^2$ ,

  $\begin{array}{l}y=\frac{x^2}{36}\\ y=\frac{1}{4\times 9}{x}^2\end{array}$

Where $p=9$ , therefore the focus is $(0,9)$ .

The directrix of the equation is $y=-p=-9$ .

The axis of symmetry is $x=0$ .