SOLUTION: How do I eliminate theta from these two equations? x = 3cos(2theta) + 1 y = 2sin(theta)

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Question 998054: How do I eliminate theta from these two equations?
x = 3cos(2theta) + 1
y = 2sin(theta)
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Given (let's call theta q)
x = 3cos(2q) + 1
y = 2sin(q)
the plan is to substitute the identity for cos(2q) that involves only sines... that is 1 - 2sin^2(q)...so that
x = 3(1 - 2sin^2(q)) + 1
We can get a value for sin(q) from the second equation...
sin(q) = y/2
Now plug that in and get
x = 3(1 - 2(y/2)^2) + 1
x = 3 - 6(y^2/4) + 1
x = 4 - 3y^2/2
It's a parabola.