Question

The abscissa of the point on the curve 3y = 6x – 5x³, the normal at which passes through origin is ______.

Options

• 1

• `1/3`

• 2

• `1/2`

Answer 1

The abscissa of the point on the curve 3y = 6x – 5x³, the normal at which passes through origin is 1.

Explanation:

Let (x₁, y₁) be the point on the given curve 3y = 6x – 5x³ at which the normal passes through the origin.

Then we have `("dy"/"dx")_(x_1, y_1)`

= `2 - 5x_1^2`.

Again the equation of the normal at (x₁, y₁) passing through the origin gives `2 - 5x_1^2`

= `(-x_1)/y_1`

= `(-3)/(6 - 5x_1^2)`.

Since x₁ = 1 satisfies the equation.