A) \[\left( \frac{7}{2},\frac{1}{4} \right)\]
B) \[\left( \frac{1}{4},\frac{7}{2} \right)\]
C) \[\left( -\frac{1}{8},7 \right)\]
D) \[\left( \frac{1}{8},-7 \right)\]
Correct Answer: D
Solution :
Here, curve is \[y={{x}^{2}}-5x+5\]\[\Rightarrow \]\[\frac{dy}{dx}=2x-5\] Since, the tangent is parallel to the line \[2y=4x+1\] \[\therefore \]\[\frac{dy}{dx}=2x-5=2\]\[\Rightarrow \]\[x=\frac{7}{2}\] When \[x=\frac{7}{2},y={{\left( \frac{7}{2} \right)}^{2}}-5\times \frac{7}{2}+5=\frac{-1}{4}\] \[\therefore \]Equation of tangent at \[\left( \frac{7}{2},\frac{-1}{4} \right)\]is \[\left( y+\frac{1}{4} \right)=2\left( x-\frac{7}{2} \right)\]\[\Rightarrow \]\[y-2x+\frac{29}{4}=0\] Only the point in option i.e., \[\left( \frac{1}{8},-7 \right)\]satisfies the above equation.
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