A) \[\frac{1}{\sqrt{5}}\]
B) \[\frac{2}{\sqrt{5}}\]
C) \[\frac{2}{\sqrt{3}}\]
D) \[\frac{1}{2}\]
Correct Answer: B
Solution :
\[y={{e}^{2x}}\,+{{x}^{2}}\] At, \[x=0,\,\,y=1\] Now, \[{{\left. \frac{dy}{dx} \right]}_{(0,1)}}\,=2{{e}^{2x}}\,+2x=2\] \[\therefore \] Equation of normal at (0, 1) is \[\therefore \,\,\,(y-1)\,=\frac{1}{2}\,(x-0)\,\,\Rightarrow \,x+2y-2=0\] So, required distance from (0, 0) is \[=\frac{|0+0-2|}{\sqrt{5}}\,=\frac{2}{\sqrt{5}}\]You need to login to perform this action.
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