The order of the differential equation of the family of all circles in the xy-plane is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3
The order of the differential equation of a family of curves equals the number of arbitrary constants in the equation of the family.
A circle with centre (h, k) and radius r is
\((x - h)^2 + (y - k)^2 = r^2\)
For the family of all circles, h, k and r can all take any values. These are 3 arbitrary constants, so three differentiations are needed to remove them, and the order is 3.