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Question: Answered & Verified by Expert
The parametric equations of the ellipse whose foci are -3,0,9,0 and eccentricity is 13, are
MathematicsEllipseTS EAMCETTS EAMCET 2022 (18 Jul Shift 1)
Options:
  • A x=3+122cosθ,y=18sinθ
  • B x=3+18cosθ,y=122sinθ
  • C x=18cosθ,y=3+122sinθ
  • D x=3+42cosθ,y=18sinθ
Solution:
2459 Upvotes Verified Answer
The correct answer is: x=3+18cosθ,y=122sinθ

Given,

Foci of ellipse 3,0 & 9,0, now this is form of shifted ellipse,

So assuming foci as h-ae,0 & h+ae,0,

So on comparing we get, h-ae=-3h-a3=-3 ...........1

And h+ae=h+a3=9 ...........2

Now on solving equation 1 & 2 we get,

a=18 & h=3

Now using formula b2=a21-e2 we get, b=122

So, parametric points will be given by h+acosθ,bsinθ3+18cosθ,122sinθ

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