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Q.
The eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ which passes through the points $(3,0)$ and $(3 \sqrt{2}, 2)$, is
Conic Sections
Solution:
Given that the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}-1$ is passing through the points $(3,0)$ and $(3 \sqrt{2}, 2)$, so we get $a^2=9$ and $b^2=4$.
Again, we know that $b^2=a^2\left(e^2-1\right)$. This gives
$4 =9\left(e^2-1\right)$
or $e^2 =\frac{13}{9} $
or $e =\frac{\sqrt{13}}{3}$