If every line of slope 2 meets a 2 x 2 − b 2 y 2 = 1 in at most one point, find its eccentricity.

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MathematicsHyperbolaAsymptotesMedium2 minQB

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If every line of slope 2 meets $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ in at most one point, find its eccentricity.

Answer:

Solution:

Substitute $y = 2 x + c$ . The quadratic coefficient must vanish for all $c$ , so $b^{2} = 4 a^{2}$ . Hence $e = 1 + b^{2} / a^{2} = 5$ .

Stream:JEESubject:MathematicsTopic:HyperbolaSubtopic:Asymptotes

⏱ 2mℹ️ Source: QB

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