A) \[x-2y=2\]
B) \[x-2y+2=0\]
C) \[2x+y=0\]
D) \[2x+y-4=0\]
Correct Answer: A
Solution :
Given, curve is\[y=x(2-x)\] \[\Rightarrow \] \[y=2x-{{x}^{2}}\] \[\frac{dy}{dx}=2-2x\] At \[(2,0)\] \[{{\left( \frac{dy}{dx} \right)}_{(2,0)}}=2-4=-2\] Equation of normal is \[{{\left( \frac{dy}{dx} \right)}_{({{x}_{1}},{{y}_{1}})}}(y-{{y}_{1}})+(x-{{x}_{1}})=0\] \[\Rightarrow \] \[-2(y-0)+(x-2)=0\] \[\Rightarrow \] \[-2y+x-2=0\] \[\Rightarrow \] \[x-2y=2\]
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