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Answer 1 · 2016-10-10T22:18:52

#(y/(3x))^2 + (x/2)^2 = 1 #

#x = 2 cos theta, implies color(red)( cos theta = x/2)#

AND

#y = 3 sin 2 theta #

#= 3 (2sin theta cos theta) #

#= 6 sin theta cos theta #

#= 6 sin theta * x/2 #

#= 3x sin theta #

So

#sin theta = color(red)(y/(3x))#

using the ID: #sin^2 theta + cos^2 theta = 1#, we have:

#(y/(3x))^2 + (x/2)^2 = 1 #