Question

The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is ______.

विकल्प

• `x^2 dy/dx - y` = 0

• `x dy/dx + 2y` = 0

• `x dy/dx` = 2y

• `x^3 dy/dx` = 3y

Answer 1

The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is `underlinebb(x dy/dx = 2y)`.

Explanation:

The general equation of a parabola having vertex at the origin and axis along positive Y-axis is

x² = 4ay  ...(i)

On differentiating equation (i), we get

2x = `4a dy/dx`

`\implies dy/dx = x/(2a)`

`\implies` 2a = `x/(dy/dx)`

Putting the value of 2a in equation (i), we get

x² = `2(x/(dy/dx))y`

`\implies x dy/dx` = 2y