Question

The order of the differential equation of all parabolas, whose latus rectum is 4a and axis parallel to the x-axis, is ______.

Options

• one

• four

• three

• two

Answer 1

The order of the differential equation of all parabolas, whose latus rectum is 4a and axis parallel to the x-axis, is two.

Explanation:

Equation of parabola whose axis is parallel to X axis and latus rectum is 4a

(y – k)² = 4a(x – h)

(where h and k are arbitrary constants)

differentiating both sides, we get

2(y – k)y' = 4ax   .......(i)

again differentiating both sides, we get

(y – k)y" + y'² = 2a

`\implies (2ax)/y^' . y^('') + y^('2)` = 2a     from (i)

`\implies 2axy^('') + y^('3)` = 2ay'

`\implies` order 2.