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

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$(3 + 8 \cos θ, 4 \sqrt{3} \sin θ)$

none of these

$(8 \cos θ, 4 \sqrt{3} \sin θ)$

$(3 + 4 \sqrt{3} \cos θ, 8 \sin θ)$

answer is A.

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Detailed Solution

Distance between two foci = 8

$\Rightarrow 2 a e = 8 \Rightarrow a e = 4 \Rightarrow a = 8 (∵ e = \frac{1}{2})$

Now, $b^{2} = a^{2} (1 - e^{2}) \Rightarrow b^{2} = 48 \Rightarrow b = 4 \sqrt{3}$

The centre of the ellipse is the mid-point of the line joining two focus

Therefore, the coordinates of the centre are (3, 0). So, the

equation of the ellipse is

$\frac{(x - 3)^{2}}{8^{2}} + \frac{(y - 0)^{2}}{(4 \sqrt{3})^{2}} = 1$

Hence, the parametric coordinates of a point on (i) are

$(3 + 8 \cos θ, 4 \sqrt{3} \sin θ)$

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