Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeTangents & NormalsEasy2 minPYQ_2023

MathematicsEasysingle choice

The two curves $x^{3} - 3 x y^{2} + 2 = 0$ and $3 x^{2} y - y^{3} - 2 = 0$

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Solution:

We have $x^{3} - 3 x y^{2} + 2 = 0$ ...(1) and $3 x^{2} y - y^{3} - 2 = 0$ ...(2) Diff. (1) and (2) w.r.t. $x$ , we obtain $(\frac{d y}{d x})_{C_{1}} (\frac{d y}{d x})_{C_{2}} = \frac{x ^{2} - y ^{2}}{2 x y} and = \frac{- 2 x y}{x ^{2} - y ^{2}}$ Since $m_{1} \times m_{2} = - 1$ , therefore the two curves cut at right angles.

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

⏱ 2mℹ️ Source: PYQ_2023

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