99 Percentile Qs Bank for JEE MainMathematicsEllipse

The length of the latus rectum of an ellipse is 18 5 and eccentricity is 4 5 , then equation of the ellipse is…

Options

Ax 2 25 + y 2 8 = 1
Bx 2 25 + y 2 9 = 1
Cx 2 25 + y 2 16 = 1
Dx 2 16 + y 2 9 = 1

Correct answer

B. x 2 25 + y 2 9 = 1

Step-by-step solution

Given, 2 b 2 a = 18 5 ⇒ b 2 a = 9 5 ⇒ b 2 = 9 5 a …(i) and, e = 1 - b 2 a 2 = 4 5 ⇒ 1 - b 2 a 2 = 16 25 ⇒ b 2 a 2 = 1 - 16 25 = 9 25 ⇒ 9 5 a a 2 = 9 25 ⇒ 9 5 a = 9 25 ⇒ a = 5 ∴ b 2 = 9 5 5 = 9 [using Eq. (i)] ∴ Required equation of ellipse, x 2 25 + y 2 9 = 1

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