Question

The order of the differential equation of all circles of radius r, having centre on X-axis and passing through the origin is ______.

Options

• 1

• 2

• 3

• 4

Answer 1

The order of the differential equation of all circles of radius r, having centre on X-axis and passing through the origin is 1.

Explanation:

The equation of a family of circles of radius r passing through the origin and having centre on X-axis is (x – r)² + (y – 0)² = r² or x² + y² – 2rx = 0. 

Since this equation has one arbitrary constant, its order is 1.