Question

The differential equation $y\frac{dy}{dx}=a-x$ represents

• A. a family of circles with centre on y-axis
• B. a family of circles with centre at origin
• C. a family of circles with given radius
• D. a family of circles with centre on x-axis

Answer 1

Answer: (D)

a family of circles with centre on x-axis

Given: $y\frac{dy}{dx}=a-x$

Integrating on both sides

$\int ydx=\int adx-\int xdx$

$\frac{y^2}{2}=ax-\frac{x^2}{2}+c$

$x^2+y^2-2ax+c=0$

${(x-a)}^2+y^2=r^2$

Hence family of circles with centre on x axis