A) cut at right angles
B) touch each other
C) cut at an angle\[\pi /3\]
D) cut at an angle\[\pi /4\]
Correct Answer: A
Solution :
Given curves are \[{{x}^{3}}-3x{{y}^{2}}+2=0\] ... (i) and \[3{{x}^{2}}y-{{y}^{3}}-2=0\] ... (ii) On differentiating Eqs. (i) and (ii), with respect to\[x\], we get \[\left( \frac{dy}{dx} \right){{c}_{1}}=\frac{{{x}^{2}}-{{y}^{2}}}{2xy}\] and \[\left( \frac{dy}{dx} \right){{c}_{2}}=\frac{2xy}{{{x}^{2}}-{{y}^{2}}}\] \[{{\left( \frac{dy}{dx} \right)}_{{{C}_{1}}}}\times {{\left( \frac{dy}{dx} \right)}_{{{C}_{2}}}}=-1\]
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