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

Options

A. 1,2
B. 2,3
C. 2,1
D. 1,1

Answer

A

Explanation

The parametric form of the given equation is `x=t, y=t^(2)`.
Differentiating, we get `2t=y_(1)`.
Putting this value in the equation of tangent, we get
`2xy_(1)//2=y+(y_(1)//2)^(2)`
or `4xy_(1)=4y+y_(1)^(2)`
The order of this equation is one and degree is two.