# 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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