Question

The degree and order of the differential equation of all tangent lines to the parabola $x^2=4y$ is

• A. $2,1$
• B. $2,2$
• C. $1,3$
• D. $1,4$

Answer 1

The correct option is A $2,1$

let $y=mx-a{m}^2$ is tangential $x^2=4y$

$\therefore a=1$

$y=mx-m^2$

$\frac{dy}{dx}=m$ ...(i)

$x\frac{dy}{dx}=mx$

$\Rightarrow x\frac{dy}{dx}=y+m^2$

$\Rightarrow x\frac{dy}{dx}=y+{\left(\frac{dy}{dx}\right)}^2$

$\therefore$ order $=1$, Degree$=2$