Question

The order of the differential equation of all circles of radius $r$, having a centre on the $y$-axis and passing through the origin is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A

$1$

Explanation for the correct option

The equation of a family of circles of radius $r$, having a centre on the $y$-axis and passing through the origin is

$$\begin{gathered} {\left(x-0\right)}^{\mathbf{2}}\mathbf{+}{\left(y-r\right)}^{\mathbf{2}}\mathbf{=}{\mathit{r}}^{\mathbf{2}} \\ \Rightarrow x^2+y^2-2ry=0 \end{gathered}$$

This is $1$ parameter family of circle.

So the order of the differential equation is $1$

Hence, the correct option is $\left(\mathrm{A}\right)$