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Mathematics - Hyperbola Question with Solution | TestHub

MathematicsHyperbolaTangent to hyperbolaHard3 minQB

MathematicsHardmultiple choice

The tangent at the point of abscissa $513 /2$ on $x^{2} /25 - y^{2} /16 = 1$ meets $x^{2} + y^{2} = 25/2$ at ordinates $β, δ$ . The harmonic mean of $β, δ$ is greater than which values?

Options:(select one or more)

Answer:

C, D

Solution:

The point has ordinate -6 and its tangent is $13 x /10 + 3 y /8 = 1$ . Intersecting with $x^{2} + y^{2} = 25/2$ and using Vieta gives harmonic-mean magnitude 6, greater than 5 and 4.

Stream:JEESubject:MathematicsTopic:HyperbolaSubtopic:Tangent to hyperbola

⏱ 3mℹ️ Source: QB

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