Question:medium

The ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ ($b>a$) is an ellipse with eccentricity $\frac{1}{\sqrt{2}}$. If the angle of intersection between the ellipse and parabola $y^2=4ax$ is $\theta$, then the coordinates of the point $\frac{20}{3}$ on the ellipse is

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When a problem in a competitive exam seems inconsistent or has typos, first try to identify the most likely intended question. If that fails, checking which of the options satisfy some part of the question's conditions can sometimes lead to the keyed answer, even if the problem is flawed.

Updated On: Mar 30, 2026

$(\frac{a}{2}, \frac{a}{2})$
$(\frac{a}{2}, \frac{3a}{2})$
$(\frac{\sqrt{5}a}{2}, \frac{3\sqrt{5}a}{2\sqrt{2}})$
$(\frac{a}{\sqrt{2}}, \frac{\sqrt{3}a}{\sqrt{2}})$

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The Correct Option is D

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