The order of the differential equation of the family of all ellipses having centre at the origin and axes along the coordinate axes is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2
Every such ellipse has an equation of the form
\( \displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \)
with two arbitrary constants a and b, which cannot be combined into one.
The differential equation of a family is obtained by differentiating as many times as there are arbitrary constants, and eliminating them. So the order equals the number of arbitrary constants:
\( \text{order} = 2 \)