How do I convert this to polar?

Question

#x=y^2/4#

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Answer 1 · 2018-05-03T19:01:22

#=>r = 4 cos theta csc^2 theta#

Polar conversion is done using:

#x equiv rcos theta#
#y equiv r sin theta#

Given

#x = y^2/4#

We can substitute in our relations

#r cos theta = (r sin theta)^2/4#

Solving for #r#, as that's usually a useful form

#4 r cos theta = r^2 sin^2 theta#

#4 cos theta = r sin^2 theta#

#r = 4 (cos theta)/(sin^2 theta)#

#=>r = 4 cos theta csc^2 theta#