Question

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):
x² + y² = a²

Answer 1

The equation of the family of curves is \[x^2 + y^2 = a^2...........(1)\]
where `a` is a parameter.
As this equation has only one arbitrary constant, we shall get a differential equation of first order.
Differentiating (1) with respect to x, we get
\[2x + 2y\frac{dy}{dx} = 0\]
\[ \Rightarrow x + y\frac{dy}{dx} = 0\]
It is the required differential equation.