InterviewSolution
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InterviewSolution
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The parametric representation of a point on the ellipse whose foci are (-1, 0) and (7, 0) and eccentricity 1/2, isA. `(3+8cos theta, 4sqrt3 sintheta)`B. `(8cos theta, 4sqrt3 sintheta)`C. `(3+4sqrt3 cos theta, 8 sin theta)`D. None of the above |
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Answer» Correct Answer - B 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)`. |
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