For the hyperbola c o s 2 α x 2 − s i n 2 α y 2 = 1 , which of the following remains constant when α varies?

a 2 = cos 2 α and b 2 = sin 2 α Coordinates of focii are ( ± a e , 0 ) ∴ b 2 = a 2 ( e 2 − 1 ) ⇒ e = sec α . Hence abscissae of foci remain constant when α varies.

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Mathematics - Hyperbola Question with Solution | TestHub

MathematicsHyperbolaGeneralMedium2 minPYQ_2007

MathematicsMediumsingle choice

For the hyperbola $\frac{x ^{2}}{c o s ^{2} α} - \frac{y ^{2}}{s i n ^{2} α} = 1$ , which of the following remains constant when $α$ varies?

Options:

Answer:

Solution:

$a^{2} = cos^{2} α$ and $b^{2} = sin^{2} α$ Coordinates of focii are $(\pm a e, 0)$ $∴ b^{2} = a^{2} (e^{2} - 1) \Rightarrow e = sec α$ . Hence abscissae of foci remain constant when $α$ varies.

Stream:JEESubject:MathematicsTopic:HyperbolaSubtopic:General

⏱ 2mℹ️ Source: PYQ_2007

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