# The differential equation of the family of curves,

Question:

The differential equation of the family of curves, $x^{2}=4 b(y+b), b \in R$, is

1. $x\left(y^{\prime}\right)^{2}=x+2 y y^{\prime}$

2. $x\left(y^{\prime}\right)^{2}=2 y y^{\prime}-x$

3. $x y^{\prime \prime}=y^{\prime}$

4. $x\left(y^{\prime}\right)^{2}=x-2 y y^{\prime}$

Correct Option: 1

Solution: