y^2 = a (b^2 – x^2)

Question

Form a differential equation representing the given family of curves by eliminating arbitrary constant a and b.

y2 = a (b2 – x2)

Answer 1

y2 = a (b2 – x2)

Differentiating w.r.t x, we get

= yy, = -ax ………(1)

differentiating again

yy2 + yy1 = -a …(2)

putting value of (-a) from (2) in (1)

yy1= (yy2 + y1y1) x

⇒ yy, = x (y12 + yy2) which is required differential equation.