Question

The order of the differential equation of all tangent lines to the parabola y = x² is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (A)

1

Answer 2

The parametric form of the given equation is x = t, y = t². The equation of any tangent at t is 2xt = y + t². Differentiating we get 2t = y₁$\left( = \frac{dy}{dx} \right)$ Putting this value in the above equation, we have 2x$\frac{y_{1}}{2}$ = y + $\left( \frac{y_{1}}{2} \right)^{2}$ ⇒ 4xy₁ = 4y + y₁².

The order of this equation is 1.