QJEEM20Mab1fc: JEE Main 2020 Mathematics - Class 11 JEEM20Mab1fc Solution: If e 1 and e 2 are the eccentricities of the ellipse, and the…

Question

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If e₁ and e₂ are the eccentricities of the ellipse,

{{{x^2}} \over {18}} + {{{y^2}} \over 4} = 1

and the hyperbola,

{{{x^2}} \over 9} - {{{y^2}} \over 4} = 1

respectively and (e₁, e₂) is a point on the ellipse, 15x² + 3y² = k, then k is equal to :

Accepted Answer

e₁ =

\sqrt {1 - {4 \over {18}}}

=

{{\sqrt 7 } \over 3}

e₁ =

\sqrt {1 + {4 \over 9}}

=

{{\sqrt {13} } \over 3}

\because

(e₁, e₂ ) lies on 15x² + 3y² = k

\therefore

15\left( {{7 \over 9}} \right) + 3\left( {{{13} \over 9}} \right)

= k

\Rightarrow

k = 16

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