Question

Transform the polar equation to cartesian equation.

$\sqrt{r}\cos \theta =\sqrt{a}$.

Answer 1

Given the polar equation,

$\sqrt{r}\cos \theta =\sqrt{a}$

Now squaring both sides we get,

$r{\cos }^2\theta =a$

Now multiplying both sides with $r$ we get,

$r^2{\cos }^2\theta =ar$

or, $\left(r\cos \theta \right)=a\sqrt{x^2+y^2}$

or, $x^2=a\sqrt{x^2+y^2}$. [ Since $x=r\cos \theta$ and $r=\sqrt{x^2+y^2}$]

This is the required transformed cartesian equation.