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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeTangents & NormalsHard2 minQB

MathematicsHardmultiple choice

The curves $y^{2} = 4 a x$ and $x y = b$ , with $a, b > 0$ , cut orthogonally. Which parameter pairs satisfy this?

Options:(select one or more)

Answer:

B, C

Solution:

The slopes are $2 a / y$ and $- y / x$ . Orthogonality gives $x = 2 a$ . Combining this with the two curve equations gives $\underline{b^{2} = 32 a^{4}}$ . Both $(1/2, 2)$ and $(1/4, 1/ (22))$ satisfy this relation; the other pairs do not.

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Tangents & Normals

⏱ 2mℹ️ Source: QB

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