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The foci of a hyperbola coincide with the foci of the ellipse x2/25 + y2/9 = 1 Find the equation of the hyperbola, if the eccentricity is 2 :

(a) 3x2 − y2 = 12 

(b) 3x2 + y2 = 12 

(c) y2 − 3x2 = 12 

(d) none of these 

1 Answer

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Best answer

Correct option (a) 3x2 − y2 = 12

Explanation:

The equation of the ellipse is of the form 

Thus, foci of the ellipse are (± ae, 0), i.e. (± 4, 0). 

Consequently, the foci of the hyperbola are (±4, 0). Now, c = 4 ⇒ ae ′ = 4 

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