gaokao 2015 Q6

gaokao · China · tianjin-science 5 marks Conic sections Equation Determination from Geometric Conditions
Given the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ $(a > 0, b > 0)$, one of its asymptotes passes through the point $(2, \sqrt{3})$, and one focus of the hyperbola lies on the directrix of the parabola $y^2 = 4\sqrt{7}x$. Then the equation of the hyperbola is
(A) $\frac{x^2}{21} - \frac{y^2}{28} = 1$
(B) $\frac{x^2}{28} - \frac{y^2}{21} = 1$
(C) $\frac{x^2}{3} - \frac{y^2}{4} = 1$
(D) $\frac{x^2}{4} - \frac{y^2}{3} = 1$
Given the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ $(a > 0, b > 0)$, one of its asymptotes passes through the point $(2, \sqrt{3})$, and one focus of the hyperbola lies on the directrix of the parabola $y^2 = 4\sqrt{7}x$. Then the equation of the hyperbola is

(A) $\frac{x^2}{21} - \frac{y^2}{28} = 1$

(B) $\frac{x^2}{28} - \frac{y^2}{21} = 1$

(C) $\frac{x^2}{3} - \frac{y^2}{4} = 1$

(D) $\frac{x^2}{4} - \frac{y^2}{3} = 1$