A hyperbola has its centre at the origin, passes through the point 4 , 2 and has transverse axis of length 4 along the x - a x i s . Then the eccentricity of the hyperbola is:

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TestHub · Accepted Answer

Equation of hyperbola having tranverse axis along $x - a x i s$ is $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$

From the given information, equation of hyperbola can be taken as

$\frac{x^{2}}{4} - \frac{y^{2}}{b^{2}} = 1,$ since $a = 2$

Since it passes through $(4, 2),$

Hence $b^{2} = \frac{4}{3}$

Now $e = \sqrt{1 + \frac{b^{2}}{a^{2}} =} \sqrt{1 + \frac{1}{3}} = \frac{2}{\sqrt{3}}$

Mathematics - Hyperbola Question with Solution | TestHub

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