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

Question

TestHub · Accepted Answer

The parametric form of the given equation is $x = t, y = t^{2}$ . The equation of any tangent at t is $2 x t = y + t^{2}$ , Differentiating we get $2 t = y_{1} (= \frac{d y}{d x})$ putting this value in the above equation, we have $2 x \frac{v _{1}}{2} = y + (\frac{y _{1}}{2})^{2} \Rightarrow 4 x y_{1} = 4 y + y_{1}^{2}$

The order of this equation is 1

Hence (A) is the correct answer

Mathematics - Differential Equation Question with Solution | TestHub

Options:

Doubts & Discussion