Question

The equation of normal to the curve y = log_e x at the point P(1, 0) is ______.

Options

• 2x + y = 2

• x - 2y = 1

• x - y = 1

• x + y = 1

Answer 1

The equation of normal to the curve y = log_e x at the point P(1, 0) is x + y = 1.

Explanation:

We have, y = log_e x `=> "dy"/"dx" = 1/x`

∴ Slope of normal at P(1, 0)

`= - 1/("dy"/"dx")_((1, 0)`

`= (- 1)/1` = - 1

∴ Equation of normal at P(1, 0)

⇒ y - 0 = (- 1)(x - 1)

⇒ y = - x + 1

⇒ x + y = 1