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The differential equation of the family of ellipses with centre at the origin and the ends of the major axis being ± 1,0 is of the degree

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

A. 1

Step-by-step solution

The general equation of the family is x 2 + y 2 a 2 = 1 … … . . i Differentiating w.r.t. x , we get 2 x + 2 y y ' a 2 = 0 ⇒ x = − y ′ y a 2 ⇒ a 2 = − y ′ x Putting in (i), we have x 2 + y 2 − x y y ′ = 1 or x 2 − x y y ′ = 1 Which is of the degree ‘ 1 ’

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