Question

convert x^2 + y^2 = 8 to a polar equation

Answer 1

Answer:

$r=\sqrt{8}$

Step-by-step explanation:

The given equation is $x^2+y^2=8$

To convert from rectangular coordinates to polar coordinates, we substitute

$x=r\cos(\theta)$ and $y=r\sin(\theta)$.

This implies that;

$(r\cos(\theta))^2+(r\sin(\theta))^2=8$

$(r^2\cos^2(\theta)+r^2\sin^2(\theta)=8$

Factor $r^2$ to get;

$r^2(\cos^2(\theta)+\sin^2(\theta))=8$

Recall that; $\cos^2(\theta)+\sin^2(\theta)=1$

$\Rightarrow r^2(1)=8$

$\Rightarrow r^2=8$

$\Rightarrow r=\sqrt{8}$

Answer 2

Answer:

r = 8 sin θ is the polar equation