If the curve has slope − 1/2 at (9, 0), then a tangent belonging to the family of lines is

Question

Let y = a√x + bx be curve, (2x − y) + λ(2x + y − 4) = 0 be family of lines.

If the curve has slope − 1/2 at (9, 0), then a tangent belonging to the family of lines is

(A) x + 2y − 5 = 0

(B) x − 2y + 3 = 0

(C) 3x − y − 1 = 0

(D) 3x + y − 5 = 0

Answer 1

Answer is (B) x − 2y + 3 = 0

Putting x = 9, y = 0 in the given equation of curve, we have

Using Eqs. (1) and (2), we get

b = − 1 and a = 3

Therefore,

y = 3√x − x

Point (1, 2) lies on curve as well as it is point of intersection of family of lines.