Question

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b: $\frac{x}{a}+\frac{y}{b}=1$

Answer 1

$\frac{x}{a}+\frac{y}{b}=1$

Differentiating both sides of the given equation with respect to x, we get:

$\frac{1}{a}+\frac{1}{b}\frac{dy}{dx}=0$

$\frac{1}{a}+\frac{1}{b}y=0$

Again, differentiating both sides with respect to x, we get:

$0+\frac{1}{b}y=0$

$\frac{1}{b}y=0$

$y=0$
Hence,the required differential equation of the given curve is y=0.