The degree and order of the differential equation of all tangent line…

Equation of any tangent to $x^2=4 y$ is $x=m y+\frac{1}{m}$, where $m$ is arbitrary constant.

$\Rightarrow 1=m \frac{d y}{d x} \Rightarrow m=\frac{1}{\frac{d y}{d x}}$

∴ Putting this value of m in $x=m y+\frac{1}{m}$, we get

$x=\frac{y}{\frac{d y}{d x}}+\frac{d y}{d x} \Rightarrow\left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}+y=0$

Which is a differential equation of order 1 and degree 2.

Hence (1) is the correct answer.