Question

The foci of a hyperbola coincide with the foci of the ellipse: x²/25 + y²/9 =1; find the equation of hyperbola if its eccentricity is 2.

Answer 1

The equation of the ellipse is

Therefore, a² = 25 and b² = 9

Let ‘e’ be the eccentricity of the ellipse

So, the co ordinates of the foci of the ellipse are (± ae, 0) i.e., (± 4, 0)

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

The co-ordinates of the foci of the hyperbola are (± a'e', 0) or (± 4, 0)

It is given that e'= 2

Therefore, a'x 2 = 4 i.e., a'= 2 or a^'2 = 2² = 4

Therefore, the required equation of the hyperbola is