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Question

Write the parametric equation of ellipse (x3)225+(y+2)216=1.

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Solution

Given equation of ellipse is (x3)225+(y+2)216=1
let X=x3,Y=y+2
X252+Y242=1
This is in the form of the ellipse x2a2+y2b2=1
a=5,b=4
The parametric equation of this ellipse is x=acosθ,y=bsinθ
X=5cosθ,Y=4sinθ
x3=5cosθ,y+2=4sinθ
x=3+5cosθ,y=2+4sinθ

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