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


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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