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$If e_{1} and e_{2} are the eccentricities of the ellipse, \frac{x^{2}}{18} + \frac{y^{2}}{4} = 1 and the hyperbola, \frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$
$respectively and (e_{1}, e_{2}) is a point on the ellipse, 15 x^{2} + 3 y^{2} = k, then k is equal to:$

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Correct option is B

We have e1=1-418=79 and e2=1+49=139 Given e1,e2 lie on 15x2+3y2=k⇒15e12+3e22=k⇒k=1579+3139=16

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If e1 and e2 are the eccentricities of the ellipse, x218+y24=1 and the hyperbola, x29-y24=1 respectively and e1,e2 is a point on the ellipse, 15x2+3y2=k, then k is equal to:

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$If e_{1} and e_{2} are the eccentricities of the ellipse, \frac{x^{2}}{18} + \frac{y^{2}}{4} = 1 and the hyperbola, \frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$
$respectively and (e_{1}, e_{2}) is a point on the ellipse, 15 x^{2} + 3 y^{2} = k, then k is equal to:$