If e 1 and e 2 are the eccentricities of the ellipse x 2 18 + y 2 4 = 1 and the hyperbola x 2 9 - y 2 4 = 1 respectively and e 1 , e 2 is a point on the ellipse 15 x 2 + 3 y 2 = k , then the value of k is equal to

Question

If e 1 and e 2 are the eccentricities of the ellipse x 2 18 + y 2 4 = 1 and the hyperbola x 2 9 - y 2 4 = 1 respectively and e 1 , e 2 is a point on the ellipse 15 x 2 + 3 y 2 = k , then the value of k is equal to, 16, 17, 15, 14

MARKS App · Accepted Answer

e 1 = 1 - 4 18 = 7 9 = 7 3 e 1 = 1 + 4 9 = 13 9 = 13 3 Also, 15 e 1 2 + 3 e 2 2 = k ⇒ k = 15 7 9 + 3 13 9 ∴ k = 16

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