Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is A 1

The parametric form of the given equation is $x=t,y=t^2$.The equation of any tangent at t is $2xt=y+t^2$, Differentiating we get $2t=y_1(=\frac{dy}{dx})$ putting this value in the above equation, we have $2x\frac{y_1}{2}=y+{\left(\frac{y_1}{2}\right)}^2\Rightarrow 4x{y}_1=4y+y_1^2$
The order of this equation is 1
Hence (A) is the correct answer