The differential equation for the family of curves $x^2+y^2-2ay=0$ where a is an arbitrary constant is:
Answer & explanation
Correct answer: option 1
$x^2+y^2-2ay=0$ … (i)
Differentiate w. r. t. x ⇒ 2x + 2py - 2ap = 0 $⇒a=\frac{2x+2py}{2p}$ (where p = dy/dx)
Substitute the value of a in (i)
$x^2+y^2-y[\frac{2x}{p}+2y]=0$
$⇒(x^2-y^2)p=2xy$