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The equation of an ellipse whose eccentr...

The equation of an ellipse whose eccentricity is 1/2 andthe vertices are (4, 0) and (10, 0) is

A

`3x^(2)+4y^(2)-42+120=0`

B

`3x^(2)+4y^(2)+42x+120=0`

C

`3x^(2)+4y^(2)+42x+120=0`

D

`3x^(2)+4y^(2)-42x-120=0`

Text Solution

Verified by Experts

The correct Answer is:
A
Major axis ` = 6 = 2a `
` rArr a = 3 `
Also, ` e = ( 1 ) /( 2 ) rArr b = ( 3sqrt3 ) /( 2 ) `
Thus, required equation is
` ( ( x - 7 ) ^ 2 )/( 9) + ( y^ 2 ) /( (27 )/(4)) = 1 `
` rArr 3x ^ 2 + 4y ^ 2 - 42 x + 120 = 0 `
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