COMEDK Exam 2013 Solved Paper

Let P(x1,y1) be the required point. The given curve is
y=6x−x2
⇒

dy

dx

=6−2x
⇒(

dy

dx

)x1,y1=6−2x1
Since, the tangent at (x1,y1) is parallel to the line
4x−2y−1=0
∴ Slope of the tangent at (x_1,y_1)=Slope of the line
4x−2y−1=0
⇒(

dy

dx

)x1,y1=2
⇒6−2x1=2⇒x1=2
∴y1=6x1−x12=6×22=8
Thus, required point is (2,8).