Question

If the line y = 1 – x touches the curve y2 – y + x = 0, then the point of contact is

(a) (0, 1)

(b) (1, 0)

(c) (1, 1)

(d) [(1/2), (1/2)]

Answer 1

The correct option (a) (0, 1)

Explanation:

curve: y2 – y + x = 0 ......(1)

line: y = 1 – x .....(2)

∴ y2 – 1 + x + x = 0

∴ y2 + 2x – 1 = 0

i.e. 1 – 2x + x2 + 2x – 1 = 0

⇒ x2 = 0

i.e. x = 0

∴ from (2), y = 1

∴ points are (x, y) = (0, 1).