A) \[\left( \frac{1}{4},\frac{1}{2} \right)\]
B) \[\left( \frac{1}{2},\frac{1}{4} \right)\]
C) \[\left( \frac{1}{2},\frac{-1}{2} \right)\]
D) \[\left( \frac{1}{2},\frac{1}{2} \right)\]
Correct Answer: A
Solution :
Given, \[{{y}^{2}}=x\] ...(i) \[\Rightarrow \] \[2y\frac{dy}{dx}=1\] \[\Rightarrow \] \[\frac{dy}{dx}=\frac{1}{2y}=slope\] Also given, \[\theta ={{45}^{o}}\] \[\therefore \] Slope tan \[\tan \,{{45}^{o}}=1\] \[\Rightarrow \] \[\frac{1}{2y}=1\] \[\Rightarrow \] \[y=\frac{1}{2}\] From Eq. (i), if \[y=1/2,\] then \[x=\frac{1}{4}\] \[\therefore \] Required point is \[\left( \frac{1}{4},\frac{1}{2} \right),\]
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