Question

Form the differential equation of:

All circles which pass through the origin and whose centres lie on X-axis.

Answer 1

Let C (h, 0) be the centre of the circle which pass through the origin. Then radius of the circle is h.

∴ equation of the circle is (x – h)² + (y – 0)² = h²

∴ x² – 2hx + h² + y² = h²

Differentiating both sides w.r.t. x, we get

2x + 2y \(\frac{dy}{dx}\) = 2h

Substituting the value of 2h in equation (1), we get

This is the required D.E.