The point on the curve `y^(2)=x` where tangent makes `45^(@)` angle with x-axis, isA. `(1//2,1//4)`B. `(1//4,1//2)`C. `(4,2)`D. `(1,1)`

The point on the curve `y^(2)=x` where tangent makes `45^(@)` angle wi

1.	The point on the curve `y^(2)=x` where tangent makes `45^(@)` angle with x-axis, isA. `(1//2,1//4)`B. `(1//4,1//2)`C. `(4,2)`D. `(1,1)`
Answer» Correct Answer - B Let `(x_(1),y_(1) )` be the required point on the curve `y^(2)=x` Then, `((dy)/(dx))_((x_(1)","y_(1)))=1` `rArr (1)/(2y_(1))=1 " "[because y^(2)=x rArr2y(dy)/(dx)=1 rArr(dy)/(dx)=(1)/(2y)]` `rArr y_(1)=(1)/(2)` Since `(x_(1),y_(1))` lies on `y^(2)=x.` `therefore x_(1)=y_(1)^(2)rArr x_(1)=(1)/(4)` Hence, `(1//4,1//2)` is the required point.

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The point on the curve `y^(2)=x` where tangent makes `45^(@)` angle with x-axis, isA. `(1//2,1//4)`B. `(1//4,1//2)`C. `(4,2)`D. `(1,1)`

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