jee-main 2022 Q66

jee-main · India · session1_24jun_shift2 Conic sections Eccentricity or Asymptote Computation

Let the maximum area of the triangle that can be inscribed in the ellipse $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { 4 } = 1 , a > 2$, 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:
(1) $\frac { \sqrt { 3 } } { 2 }$
(2) $\frac { 1 } { 2 }$
(3) $\frac { 1 } { \sqrt { 2 } }$
(4) $\frac { \sqrt { 3 } } { 4 }$

Let the maximum area of the triangle that can be inscribed in the ellipse $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { 4 } = 1 , a > 2$, 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:\\
(1) $\frac { \sqrt { 3 } } { 2 }$\\
(2) $\frac { 1 } { 2 }$\\
(3) $\frac { 1 } { \sqrt { 2 } }$\\
(4) $\frac { \sqrt { 3 } } { 4 }$

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