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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