Question

Write the following parametric equations as a polar equation x=t^2 y=2t

Answer 1

Answer:

$r=4\csc \theta \cot\theta$

Step-by-step explanation:

The given parametric equations are;

$x=t^2$

$y=2t$

We make t the subject in the second equation to get:

$t=\frac{y}{2}$

We substitute into the first equation to get:

$x=(\frac{y}{2})^2$

We use the relation:

$x=r\cos \theta$ and $y=r\sin \theta$

$r\cos \theta=(\frac{r\sin \theta}{2})^2$

$r\cos \theta=\frac{r^2\sin^2 \theta}{4}$

$r=4\csc \theta \cot\theta$