The Foci Of A Hyperbola Coincide With The Foci Of The Ellipse . Find The Equation Of The Hyperbola If Its Eccentricity Is 2.

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Question

The foci of a hyperbola coincide with the foci of the ellipse . Find the equation of the hyperbola if its eccentricity is 2.

diffcult

Solution

Correct option is

The given ellipse is

Comparing with

.

∴ Foci of ellipse are (±ae, 0) i.e., (±4, 0)

So, the coordinates of foci of the hyperbola are (±4, 0)

Let e’ be the eccentricity of the required hyperbola and its equation be

The coordinates of foci are (±Ae’, 0)

.

Substituting the value of A and B in (i), we get

which is required hyperbola.

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