Q3 of 149 Page 16

The equation of the normal to the curve y = x (2 – x) at the point (2, 0) is

Given that y = x (2 – x)

⇒ y = 2x – x²

Slope of the tangent

Slope at (2, 0) = 2 – 4 = -2

Equation of normal:

⇒2y=x-2

⇒ x – 2y – 2 = 0

Hence option A is correct.

The equation to the normal to the curve y = sinx at (0, 0) is

The equation of the normal to the curve y = x + sin x cos x at is

The point on the curve y² = x where tangent makes 45° angle with x-axis is

If the tangent to the curve x = at², y = 2at is perpendicular to x-axis, then its point of contact is