Question

The point on the curve y² = x, where the tangent makes an angle of `pi/4` with x-axis is ______.

Options

• `(1/2, 1/4)`

• `(1/4, 1/2)`

• (4, 2)

• (1, 1)

Answer 1

The point on the curve y² = x, where the tangent makes an angle of `pi/4` with x-axis is `(1/4, 1/2)`.

Explanation:

`"dy"/"dx" = 1/(2y) = tan  pi/4` = 1

⇒ y = `1/2`

⇒ x = `1/4`