The equation(s) of the tangent(s) to the curve `y=x^(4)` from the point (2, 0) not on the curve is given by

Options

A. `y=0`
B. `x=0`
C. `x+y=0`
D. None of these

Answer

A

Explanation

Let the point of contact be `(h,k)`, then ltbrLgt `k=h^(4)`…………i
Slope of the curve
`(dy)/(dx)=4x^(3)implies((dy)/(dx))_((h//k))=4h^(3)`
`:.`Equation of tangent is
`y-k=4h^(3)(x-h)`
This equation passes through (2,0).
`:.-k=4h^(3)(2-h)`
`implies-h^(4)=8h^(3)-8h^(4)` [from Eq. (i)]
`impliesh^(3)(3h-8)=0`
`impliesh=0` or `8/3`
`:.k=0` or `(8/3)^(4)`
`:.` Points of contact are (0,0) and `[8/3,(8/3)^(4)]`
Equation of tangents are `y=0` and
`y-(8/3)^(4)=4(8/3)^(3)(x-8/3)`