Question

Find the equivalent cartesian form of the polar equation $\sqrt{r}\cos \theta =\sqrt{a}$.

Answer 1

Given the polar equation

$\sqrt{n}\cos \theta =\sqrt{\alpha }$

Squaring both sides. we get

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

${\left(n\cos \theta \right)}^2=an$

$x^2=a{(x^2+y^2)}^{1/x}[\because x=n\cos \theta ]$

squaring both sides we get

$x^4=a^2(x^2+y^2)$