A) \[(0,\,\,0)\]
B) \[(0,\,\,a)\]
C) \[(a,\,\,0)\]
D) \[(a,\,\,a)\]
Correct Answer: B
Solution :
Key Idea: The normal is parallel to \[x-\]axis, if\[\frac{dx}{dy}=0\] Given equation of curve is \[\sqrt{x}+\sqrt{y}=\sqrt{a}\] ... (i) On differentiating w.r.t.\[x,\] we get \[\frac{1}{2\sqrt{x}}+\frac{1}{2\sqrt{y}}=\frac{dy}{dx}=0\] \[\Rightarrow \] \[\frac{dx}{dy}=\sqrt{\frac{x}{y}}\] Since, the normal is parallel to\[x-\]axis. \[\therefore \] \[\frac{dx}{dy}=0\] \[\Rightarrow \] \[-\sqrt{\frac{x}{y}}=0\] \[\Rightarrow \] \[x=0\] \[\therefore \]From Eq. (i)\[y=a\] \[\therefore \]Required point is\[(0,\,\,a)\].
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