Question

Identify the graph of x= y2. Then write theequation in polar form.

Answer 1

Given the equation:

$x=y^2$

The graph of the equation will be as shown in the following picture:

Now, we will convert the equation to the polar form

We will use the following equations to convert it:

$\begin{gathered} x=r\cdot\cos \theta \\ y=r\cdot\sin \theta \end{gathered}$

Substitute with x and y, So

$\begin{gathered} x=y^2 \\ r\cdot\cos \theta=r^2\cdot\sin ^2\theta \\ r=\frac{\cos \theta}{\sin ^2\theta} \end{gathered}$