Mathematics - Hyperbola Question with Solution | TestHub

MathematicsHyperbolaMiscellaneous/MixedMedium2 minPYQ_2012

MathematicsMediumsingle choice

Find the eccentricity of the conic represented by $x^{2} - y^{2} - 4 x + 4 y + 16 = 0$

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Answer:

Solution:

We have $x^{2} - y^{2} - 4 x + 4 y + 16 = 0$ $\Rightarrow (x^{2} - 4 x) - (y^{2} - 4 y) = 16$ $\Rightarrow (x^{2} - 4 x + 4) - (y^{2} - 4 y + 4) = - 16$ $\Rightarrow (x - 2)^{2} - (y - 2)^{2} = - 16$ $\Rightarrow \frac{( x - 2 ) ^{2}}{4 ^{2}} - \frac{( y - 2 ) ^{2}}{4 ^{2}} = 1$ This is rectangular hyperbola, whose eccentricity is always $2$ .

Stream:BITSATSubject:MathematicsTopic:HyperbolaSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: PYQ_2012

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