ISC (Commerce) Class 12CISCE
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Find the Equation of an Ellipse Whose Latus Rectum is 8 and Eccentricity is `1/3` - ISC (Commerce) Class 12 - Mathematics

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Question

Find the equation of an ellipse whose latus rectum is 8 and eccentricity is `1/3`

Solution

`(2b^2)/a = 8`

`b^2 = 4a`

`e = 1/3`

`b^2 = a^2(1-e^2)`

`:. 4a = a^2 (1-(1/3)^2)`

`4a = a^2 (8/9)`

`9/2 = a`

`a^2 = 81/4`

`b^2 = 4a =  4 xx 1/2 = 18`

Equation of ellipse

`x^2/a^2 + y^2/b^2  = 1`

`(4x^2)/81 + y^2/18 = 1`

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APPEARS IN

 2014-2015 (March) (with solutions)
Question 1.2 | 3.00 marks
Solution Find the Equation of an Ellipse Whose Latus Rectum is 8 and Eccentricity is `1/3` Concept: Area Under Simple Curves.
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