If a tangent to the curve \( \Large y=6x-x^{2} \) is parallel to the line \( \Large 4x-2y-1=0 \) then the point of tangency on the curve is: ' _

A) (6, 1)

B) (8, 2)

C) (2, 8)

D) (4, 2)

Correct answer:
C) (2, 8)

Description for Correct answer:

Since, tangent is parallel to \( \Large y = 2x-\frac{1}{2} \)

Therefore, Equation of tangent is \( \Large y = 2x+h \)

The point of tangency will be the point of intersection of tangent and curve but in the given equation of options only option (a) satisfied the equation of curve then \( \Large \left(2,\ 8\right) \) will be the point oftangency.


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