Question

How do I find the polar equation for `x^2+y^2=7y`?

Answer 1

To solve this problem we need to convert all of the `x`'s and `y`'s to `r`'s and `theta`'s.

Before we look at the specifics of this problem please take a look at the relationships between the polar and rectangular coordinate systems.

Understanding these relationships are critical to better understanding how to solve these types of problems.

`x=rcos(theta)`

`y=rsin(theta)`

`y/x=tan(theta)`

`tan^1(y/x)=theta`

`x^2+y^2=r^2`

To solve this type of problem one of the first things to look for is a way to make substitutions.

`x^2+y^2=7y`

Substitute in `r^2` for `x^2+y^2`

`r^2=7y`

Substitute in `rsin(theta)` for `y`

`r^2=7rsin(theta)`

`(r^2)/r=(7rsin(theta))/r`

`r=7sin(theta) ->` is the polar form of `-> x^2+y^2=7y`