Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it ?

Engineering

Mathematics

Standard Ellipse

Question

$(4 \sqrt{3}, 2 \sqrt{3})$

$(4 \sqrt{3}, 2 \sqrt{2})$

$(4 \sqrt{2}, 2 \sqrt{3})$

$(4 \sqrt{2}, 2 \sqrt{2})$

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$\frac{2 b^{2}}{a}$ = 8 and ae = b

⇒ $\frac{a^{2} (1 - e^{2})}{a}$ = 4 and a² e² = a²(1 – e²)

a (1 – e²) = 4 ⇒ e = $\frac{1}{\sqrt{2}}$

⇒ a = 8

Ellipse : $\frac{x^{2}}{64} + \frac{y^{2}}{32}$ = 1