Question

What the eccentricity of the hyperbola with its principal axes along the

coordinate axes and which passes through (3,0) and $(3\sqrt{2},2)$

• A. $\frac{1}{3}$
• B. $\frac{\sqrt{13}}{3}$
• C. $\frac{2}{3}$
• D. $\frac{\sqrt{5}}{3}$

Answer 1

The correct option is B

$\frac{\sqrt{13}}{3}$

Its given tat the hyperbola goes through the points (3,0) and $(3\sqrt{2},2)$,

Let the hyperbola of the form,

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ .........(1)

(1) passes through $(3,0)$

$\frac{9}{a^2}=1$

$a^2=1$

(1) passes through $(3\sqrt{2},2)$

$\frac{9.2}{9}-\frac{4}{b^2}=1$

$b^2=4$

$\therefore$ The required hyperbola is,

$\frac{x^2}{9}-\frac{y^2}{4}=1$

Eccentricity is given by,

$e^2=1+\frac{b^2}{a^2}$

$=1+\frac{4}{9}=\frac{13}{9}$

$\therefore$ $e=\frac{\sqrt{13}}{3}$