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

Answer: (A)

The parametric form of the given equation is $x=t$ and $y=t^2$ . The equation of any tangent at t is $2xt=y+t^2$ On differentiating, we get $2t=y_1$ On putting this value in the equation of tangent, we have $\frac{2x{y}_1}{2}=y+{\left(\frac{y_1}{2}\right)}^2$ $\Rightarrow$ $4x{y}_1=4y+y_1^2$ So, the order of this equation is one.