Question

If a tangent to the curve y = 6x - x2 is parallel to the line 4x - 2y - 1 = 0, then the point of tangency on the curve is

(A) (2, 8)

(B) (8, 2)

(C) (6, 1)

(D) (4, 2)

Answer 1

Answer is (A) (2, 8)

Given that

y = 6x - x2 (1)

dy/dx = 6 - 2x

Since, the tangent is parallel to the line

4x - 2y - 1 = 0

Therefore,

dy/dx = 6 - 2x = -4/-2 ⇒ 6 - 2x = 2 ⇒ x = 2

Substituting the value of x in Eq. (1), we get y = 8. Hence, the required point of tangency will be (2,8).