The order anda degree of the differential equation of all tangent lines to the parabola `x^(2)=4y` is

Options

A. 1,2
B. 2,2
C. 3,1
D. 4,1

Answer

A

Explanation

The equaiton of any tangent to `x^(2)=4y` is
`x=my+(1)/(m)`, where m is an arbitrary constant.
Differentiating this w.r.t. to x, we get
`1=m(dy)/(dx)rArr m=(1)/((dy)/(dx))`
Putting the value of m in x = `my+(1)/(m)`, we get
`x=(y)/((dy)/(dx))+(dy)/(dx)rArr((dy)/(dx))^(2)-x(dy)/(Dx)+y=0`,
Which is differential equation of order 1 and degree 2.