A) \[(0,0)\]
B) \[(0,a)\]
C) \[(a,0)\]
D) \[(a,a)\]
E) \[(-a,a)\]
Correct Answer: B
Solution :
The equation of given curve is\[\sqrt{x}+\sqrt{y}=\sqrt{a}\] \[\therefore \] \[\frac{1}{2\sqrt{x}}+\frac{1}{2\sqrt{y}}\frac{dy}{dx}=0\] \[\Rightarrow \] \[\frac{dy}{dx}=-\frac{\sqrt{y}}{\sqrt{x}}\] The normal is parallel to\[x-\]axis, if \[{{\left( \frac{dx}{dy} \right)}_{({{x}_{1}},{{y}_{1}})}}=0\] \[\Rightarrow \] \[\sqrt{{{x}_{1}}}=0\] \[\Rightarrow \] \[{{x}_{1}}=0\] \[\therefore \]From equation of curve\[{{y}_{1}}=a\]. \[\therefore \]Required point is\[(0,a)\].
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