A) (0,0)
B) \[(e,\,\,e)\]
C) \[({{e}^{2}},\,2{{e}^{2}})\]
D) \[({{e}^{-2}}-2{{e}^{-2}})\]
Correct Answer: D
Solution :
\[y=x\log x\] Þ \[\frac{dy}{dx}=1+\log x\] The slope of the normal = \[-\frac{1}{(dy/dx)}=\frac{-1}{1+\log x}\] The slope of the line \[2x-2y=3\] is 1. \ \[\frac{-1}{1+\log x}=1\] Þ \[\log x=-2\] Þ \[x={{e}^{-2}}\] \ \[y=-2{{e}^{-2}}\] \ Co-ordinate of the point is \[({{e}^{-2}},\,-2{{e}^{-2}})\].
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