Question

A hyperbola whose transverse axis is along the major axis of the conic, $\frac{x^2}{3}+\frac{y^2}{4}=4$ and has vertices at the foci of this conic. If the eccentricity of the hyperbola is $\frac{3}{2}$, then which of the following points does NOT lie on it ?

• A. (0, 2)
• B. $(\sqrt{5}$, 2 $\sqrt{2})$
• C. $(\sqrt{10}$, 2 $\sqrt{3})$
• D. $(5,2\sqrt{3})$

Answer 1

Answer: (D)

ellipse $\frac{x^2}{12}+\frac{y^2}{16}=1$
foci $(0,\pm$ be $)$
$e_e=\sqrt{1-\frac{12}{16}}=\frac{1}{2}$
for hyperbola

$e_H=\frac{3}{2}$
equation $\Rightarrow \frac{x^2}{a^2}-\frac{y^2}{b^2}=-1$
$e_H=\frac{3}{2}=\sqrt{1+\frac{a^2}{b^2}}$
$\Rightarrow \frac{9}{4}-1=\frac{a^2}{b^2}$
$\frac{a^2}{b^2}=\frac{5}{4}$
$\Rightarrow a^2=5$
$\frac{x^2}{5}-\frac{y^2}{4}=-1$