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#