If e1 and e2 are the eccentricities of the ellipse, [x^2 18 + y^2 4 = 1] and the hyperbola…

Question

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

Solutions · 1