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The parametric coordinates of a point on...

The parametric coordinates of a point on the ellipse, whose foci are `(-3, 0)` and (9, 0) and eccentricity `(1)/(3)` , are

A

`(-3 +9 cos theta, 9 sin theta)`

B

`(4-3 cos theta , 4 +9 sin theta)`

C

`(3+18 cos theta , 4 +9 sin theta)`

D

`(3+18 cos theta, 12 sqrt(2) sin theta)`

Text Solution

Verified by Experts

The correct Answer is:
D
Distance between foci
`2ae=12 " "`Centre (3,0)
`implies ae =6 " "implies a=18`
`b^(2) = a^(2) (1-e^(2)) =(18)^(2)[1-(1)/(9)]`
` = 18 xx 16 implies b=12 sqrt(2)`
Equation of ellipse `((x-3)^(2))/((18)^(2)) + ((y-0)^(2))/(18 xx 16) =1`
Parametric coordinate , `x-3 = a cos `
` implies x =3 + 18 cos theta implies y-0 = sqrt(18 xx 16) * sin theta `
` implies y= 12 sqrt(2) sin theta `
`3 + 18 cos theta, 12sqrt(2) sin theta `
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