Question

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

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. $\sqrt{5}$
• D. $-\sqrt{3}$

Answer 1

The correct option is B $\sqrt{3}$

Since, given hyperbola passes through $(4,0)$ & $(3\sqrt{2},2)$
$\Rightarrow \frac{16}{a^2}-\frac{0}{b^2}=1\Rightarrow a^2=16$
And $\frac{18}{16}-\frac{4}{b^2}=1\Rightarrow b^2=32$
Hence, required eccentricity is $=\sqrt{1+\frac{b^2}{a^2}}=\sqrt{3}$