Question

The differential equation of all circles in the first quadrant which touches the coordinate axes is of order?

• A. $1$
• B. $2$
• C. $3$
• D. None of these

Answer 1

The correct option is A

$1$

Explanation for correct option:

Calculating the differential equation.

Given,

There are circles in the first quadrant that touches coordinate axes.

The diagram represents,

This circle will have the same $x,y$ coordinates and that is equal to the radius of the circle.

The equation becomes,

${\left(\mathrm{x}-\mathrm{\alpha }\right)}^2+{\left(\mathrm{y}-\mathrm{\alpha }\right)}^2={\mathrm{\alpha }}^2$

where a is a parameter.

Since there is only one parameter, the equation is of order $1$.

Therefore, the differential equation is of order $1$.

Hence, the correct answer is Option (A).