A) \[(a,\,a)\]
B) \[(2a,\,-a)\]
C) \[(2a,\,a)\]
D) None of these
Correct Answer: C
Solution :
\[{{x}^{3}}-8{{a}^{2}}y=0\] Þ \[3{{x}^{2}}-8{{a}^{2}}\,.\,\frac{dy}{dx}=0\] Þ \[3{{x}^{2}}=8{{a}^{2}}\,.\,\frac{dy}{dx}\] Þ \[\frac{dy}{dx}=\frac{3{{x}^{2}}}{8{{a}^{2}}}\] \ Slope of the normal = \[-\frac{1}{\left( \frac{dy}{dx} \right)}\] = \[-\frac{1}{\frac{3{{x}^{2}}}{8{{a}^{2}}}}\]\[=-\frac{8{{a}^{2}}}{3{{x}^{2}}}\] Given \[\frac{-8{{a}^{2}}}{3{{x}^{2}}}=\frac{-2}{3}\] \\[(x,\,y)=(2a,\,a)\].
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