The eccentricity of a hyperbola passing throu | vedclass

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(B) Let the equation of the hyperbola be $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$.Since it passes through $(3, 0)$,we have $\frac{3^2}{a^2} - \frac{0^2

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

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(B) Let the equation of the hyperbola be $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$.Since it passes through $(3, 0)$,we have $\frac{3^2}{a^2} - \frac{0^2}{b^2} = 1$,which gives $a^2 = 9$,so $a = 3$.Since it passes through $(3\sqrt{2}, 2)$,we have $\frac{(3\sqrt{2})^2}{a^2} - \frac{2^2}{b^2} = 1$.Substituting $a^2 = 9$,we get $\frac{18}{9} - \frac{4}{b^2} = 1$,which simplifies to $2 - \frac{4}{b^2} = 1$.Thus,$\frac{4}{b^2} = 1$,so $b^2 = 4$.The eccentricity $e$ of a hyperbola is given by $e = \sqrt{1 + \frac{b^2}{a^2}}$.Substituting the values,$e = \sqrt{1 + \frac{4}{9}} = \sqrt{\frac{13}{9}} = \frac{\sqrt{13}}{3}$.

The eccentricity of a hyperbola passing through the points $(3, 0)$ and $(3\sqrt{2}, 2)$ is:

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