Question

Find the eccentricity of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ which passes through (4, 0) & $(3\sqrt{2}, 2)$

Answer 1

$\sqrt{3}$

Answer 2

1. Substitute the point (4, 0) into the hyperbola equation to find $a^2 = 16$.
2. Substitute the point $(3\sqrt{2}, 2)$ and $a^2=16$ into the hyperbola equation to find $b^2 = 32$.
3. Use the formula $e^2 = 1 + \frac{b^2}{a^2}$ to calculate the eccentricity $e = \sqrt{3}$.