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

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Answer 1 · 2014-09-21T00:00:21

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 $-> x^2+y^2=7y$

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