Q5 / 53 · NTA Abhyas (JEE Main) 2020 · Mathematics · Ellipse

If $(0,3 + \sqrt{5})$ is a point on the ellipse whose foci are $(2,3)$ and $(- 2,3)$ , then the length of the semi-major axis is

Correct answer: 3

Solution

If $P$ is a point on the ellipse having $S$ & $S'$ as foci, then

$P S + P S^{'} = 2 a$
Where $2 a =$ length of the major-axis
$\Rightarrow \sqrt{2^{2} + 5} + \sqrt{2^{2} + 5} = 2 a$
$\Rightarrow a = 3$ $=$ semi-major axis

Hence, the correct answer is 3.

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Solution

More Ellipse Questions

If $(0,3 + \sqrt{5})$ is a point on the ellipse whose foci are $(2,3)$ and $(- 2,3)$ , then the length of the semi-major axis is