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