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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeTangents & NormalsMedium2 minQB

MathematicsMediumsingle choice

The curves $x^{3} - 3 x y^{2} = a$ and $3 x^{2} y - y^{3} = b$ intersect at an angle of

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Answer:

Solution:

$3 x^{2} - 3 y^{2} - 6 x y m_{1} = 0 \Rightarrow m_{1} = \frac{x ^{2} - y ^{2}}{2 x y}; 6 x y + 3 x^{2} m_{2} - 3 y^{2} m_{2} = 0 \Rightarrow m_{2} = \frac{2 x y}{y ^{2} - x ^{2}}$ Clearly $m_{1} m_{2} = - 1$

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

⏱ 2mℹ️ Source: QB

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