Question

How do you convert `2x+y^2 = 5` to polar form?

Answer 1

Please see the explanation for steps leading to the polar form:

Explanation:

Substitute `(rcos(theta))` for x and `r^2sin^2(theta)` for `y^2`:

`r^2sin^2(theta) +`2rcos(theta) - 5 = 0#

Use the positive root of the quadratic formula:

`r = {-2cos(theta) + sqrt(4cos^2(theta) + 20sin^2(theta))}/(2sin^2(theta))`

`r = {-cos(theta) + sqrt(cos^2(theta) + 5sin^2(theta))}/(sin^2(theta))`

`r = {-cos(theta) + sqrt(1 + 4sin^2(theta))}/(sin^2(theta))`