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Ellipse question

2022 · 24 Jun · Shift 2 · Q29

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PYQ Library
JEE Main
Mathematics
Ellipse
2022 · 24 Jun · Shift 2 · Q29

Ellipse question

2022 · 24 Jun · Shift 2 · Q29

JEE MainMathematicsEllipseMCQ+4 / −1

Let the maximum area of the triangle that can be inscribed in the ellipse

{{{x^2}} \over {{a^2}}} + {{{y^2}} \over 4} = 1,\,a \gt 2

, having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the y-axis, be

6\sqrt 3

. Then the eccentricity of the ellipse is :

A
${{\sqrt 3 } \over 2}$
B
${1 \over 2}$
C
${1 \over {\sqrt 2 }}$
D
${{\sqrt 3 } \over 4}$

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