"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 :"

Question

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"

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 :

Solution

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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 :

Solution

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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 :