The parametric representation of a point on the ellipse whose foci are (-1, 0) and (7, 0) and eccentricity 1/2, is

Options

A. `(3+8cos theta, 4sqrt3 sintheta)`
B. `(8cos theta, 4sqrt3 sintheta)`
C. `(3+4sqrt3 cos theta, 8 sin theta)`
D. None of the above

Answer

B

Explanation

Distance between two foci, 2ae=7+1=8
`therefore ae=4`
`Rightarrow a=8 " "(therefore e=(1)/(2)"given")`
`"Now," b^(2)=a^(2)(1-e^(2))=64(1-(1)/(4))`
`therefore b^(2)=48 Rightarrow b=4sqrt3`
Since the centre of the ellipse is the mid point of the line joining two foci, therefore the coordinates of the centre are (3,0).
Its equation is
`((x-3)^2)/(8^(2))+((y-0)^(2))/((4sqrt3)^(2))=1.....(i)`
Hence, the parametric coordinate of a point on Eq. (i) are `(3+8 costheta, 4sqrt3 sin theta)`.