KVPY Sample Paper KVPY Stream-SX Model Paper-20

The tangent to the curve \[y={{x}^{2}}-5x+5,\]parallel to the line \[2y=4x+1,\]also passes through the point:

A) \[\left( \frac{7}{2},\frac{1}{4} \right)\]

B) \[\left( \frac{1}{8},-7 \right)\]

C) \[\left( -\frac{1}{8},7 \right)\]

D) \[\left( \frac{1}{4},\frac{7}{2} \right)\]

Correct Answer: B

Solution :

\[y={{x}^{2}}-5x+5\]

\[\frac{dy}{dx}=2x-5=2\]

\[\Rightarrow \] \[x=\frac{7}{2}\] at \[x=\frac{7}{2},y=\frac{-1}{4}\]

Equation of tangent at \[\left( \frac{7}{2},\frac{-1}{4} \right)\] is

\[2x-y-\frac{29}{4}=0\]

Now check options

\[x=\frac{1}{8},y=-7.\]