Mathematics - Hyperbola Question with Solution | TestHub

MathematicsHyperbolaGeneralEasy2 minPYQ_2018

MathematicsEasysingle choice

If $e_{1}$ and $e_{2}$ are the eccentricities of a hyperbola $3 x^{2} - 3 y^{2} = 25$ and its conjugate, then

Answer:

Solution:

Given equation can be written as

$x^{2} - y^{2} = \frac{25}{3}$

$∴ e_{1} = \sqrt{1 + \frac{b^{2}}{a^{2}}}$

$= \sqrt{1 + 1} = \sqrt{2}$

The equation of conjugate hyperbola is

$- x^{2} + y^{2} = \frac{25}{3}$

$∴ e_{2} = \sqrt{1 + \frac{b^{2}}{a^{2}}} = \sqrt{1 + 1} = \sqrt{2}$

$∴ e_{1}^{2} + e_{2}^{2} = {(\sqrt{2})}^{2} + {(\sqrt{2})}^{2} = 4$

Hence, $e_{1}^{2} + e_{2}^{2} = 4$ .

Stream:BITSATSubject:MathematicsTopic:HyperbolaSubtopic:General

⏱ 2mℹ️ Source: PYQ_2018

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