# How do you convert x^2/36 + y^2/100 = 1  into polar form?

Nov 24, 2016

#### Explanation:

Substitute $r \sin \left(\theta\right)$ for y and $r \cos \left(\theta\right)$ for x:

${\left(r \cos \left(\theta\right)\right)}^{2} / 36 + {\left(r \sin \left(\theta\right)\right)}^{2} / 100 = 1$

Factor out ${r}^{2}$

${r}^{2} \left({\cos}^{2} \frac{\theta}{36} + {\sin}^{2} \frac{\theta}{100}\right) = 1$

Make a common denominator:

${r}^{2} \frac{100 {\cos}^{2} \left(\theta\right) + 36 {\sin}^{2} \left(\theta\right)}{3600} = 1$

${r}^{2} \frac{64 {\cos}^{2} \left(\theta\right) + 36 {\cos}^{2} \left(\theta\right) + 36 {\sin}^{2} \left(\theta\right)}{3600} = 1$

${r}^{2} \frac{64 {\cos}^{2} \left(\theta\right) + 36}{3600} = 1$

Divide both side by $\frac{64 {\cos}^{2} \left(\theta\right) + 36}{3600}$:

${r}^{2} = \frac{3600}{64 {\cos}^{2} \left(\theta\right) + 36}$

square root both sides:

$r = \frac{60}{\sqrt{64 {\cos}^{2} \left(\theta\right) + 36}}$