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
$x=t,y=t^2$
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 above equation, we get
$x{y}_1=y+{\left(\frac{y_1}{2}\right)}^2$
$\Rightarrow 4x{y}_1=4y+y_1^2$
The order of this equation is 1 .