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(C) The equation of a circle that lies in the first quadrant and touches both the axes is given by $(x - a)^2 + (y - a)^2 = a^2$,where $a$ is the radi

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(C) The equation of a circle that lies in the first quadrant and touches both the axes is given by $(x - a)^2 + (y - a)^2 = a^2$,where $a$ is the radius of the circle.This simplifies to $x^2 - 2ax + a^2 + y^2 - 2ay + a^2 = a^2$,which is $x^2 + y^2 - 2ax - 2ay + a^2 = 0$.Here,there is only one arbitrary constant,$a$.The order of the differential equation is equal to the number of independent arbitrary constants in the general equation of the family of curves.Since there is only $1$ arbitrary constant,the order of the differential equation is $1$.

The order of the differential equation of all circles which lie in the first quadrant and touch both the axes is...

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