Question:
The differential equation of the family of curves,
$x^{2}=4 b(y+b), b \in R$, is:
Correct Option: 1,
Solution:
Since, $x^{2}=4 b(y+b)$
$x^{2}=4 b y+4 b^{2}$
$2 x=4 b y^{\prime}$
$\Rightarrow \quad b=\frac{x}{2 y^{\prime}}$
So, differential equation is
$x^{2}=\frac{2 x}{y^{\prime}} \cdot y+\left(\frac{x}{y^{\prime}}\right)^{2}$
$x\left(y^{\prime}\right)^{2}=2 y y^{\prime}+x$
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