Mathematics

Problem

Let the eccentricity of the hyperbola

\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1

be reciprocal to that of the ellipse

x^2 + 4y^2 = 4

. If the hyperbola passes through a focus of the ellipse, then a. the equation of the hyperbola is

\frac{x^2}{3} - \frac{y^2}{2} = 1

b. a focus of the hyperbola is

(2, 0)

c. the eccentricity of the hyperbola is

\sqrt{\frac{5}{3}}

d. the equation of the hyperbola is

x^2 - 3y^2 = 3