Question

The eccentricity of the hyperbola which passes through (3, 0) and $(3\sqrt{2},2)$ is

• A. $\sqrt{(13)}$
• B. $\frac{\sqrt{13}}{3}$
• C. $\sqrt{\frac{13}{4}}$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Let equation of hyperbola is $x^{2}/a^{2} - y^{2}/b^{2} = 1$. Point (3, 0) lies on hyperbola

So, $\frac{(3)^{2}}{a^{2}} - \frac{0}{b^{2}} = 1$ or $\frac{9}{a^{2}} = 1$ or $a^{2} = 9$ and point $(3\sqrt{2},2)$ also lies on hyperbola. So, $\frac{3(\sqrt{2})^{2}}{a^{2}} - \frac{(2)^{2}}{b^{2}} = 1$

Put $a^{2} = 9$ we get, $\frac{18}{9} - \frac{4}{b^{2}} = 1$ or $2 - \frac{4}{b^{2}} = 1$ or $- \frac{4}{b^{2}} = 1 - 2$ or $\frac{4}{b^{2}} = 1$ or $b^{2} = 4$

We know that $b^{2} = a^{2}(e^{2} - 1)$. Putting values of $a^{2}$ and $b^{2}$

$4 = 9(e^{2} - 1)$ or $e^{2} - 1 = \frac{4}{9}$ or $e^{2} = 1 + \frac{4}{9}$ or

$e = \sqrt{(1 + 4/9)}\text{or}e = \sqrt{(13)/9} = \frac{\sqrt{13}}{3}$