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

Q5 of 149 Page 16

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

Given that the tangent to the curve x = at², y = 2at is perpendicular to x-axis.

Differentiating both w.r.t. t,

From y = 2at,

Slope of x axis = 0

⇒ a = 0

Then point of contact is (0, 0).

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

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

The point on the curve y = x² – 3x + 2 where tangent is perpendicular to y = x is

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