Find the polar equation of 3x2=4-3y2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 44E
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Find the polar equation of 3x2=4-3y2

I'm confused because I end up without a theta value in my answer because of trig identities and I don't think that is correct.

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