If the foci of a hyperbola are foci of the ellipse $x^2\over 25$ + $y^2\over 9$ = 1. If the eccentricity of the hyperbola be 2, then its equation is :

Solution :

For ellipse e = $4\over 5$, so foci = ($\pm$4, 0)

for hyperbola e = 2, so a = $ae\over e$ = $4\over 2$ = 2, b = $2\sqrt{4-1}$ = 2$\sqrt{3}$

Hence the equation of the hyperbola is $x^2\over 4$ – $y^2\over 12$ = 1

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