Question

An equation of the tangent to the curve $y=x^4$ from the point (2, 0) not on the curve is

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

Answer 1

The correct option is A y=0

Let the point of contact be (h,k), where k =$h^4$. Tangent is $y-k=4h^3(x-h),[\because \frac{dy}{dx}=4x^3]$
It passes through (2, 0), $\therefore -k=4h^3(2-h)$
$\Rightarrow h=0$ or $\frac{8}{3},\therefore k=0$ or $(\frac{8}{3}{)}^4$
$\therefore$ Points of contact are (0, 0) and $(\frac{8}{3},{\left(\frac{8}{3}\right)}^4)$
$\therefore$ Equation of tangents are
y=0 and $y-{\left(\frac{8}{3}\right)}^4=4{\left(\frac{8}{3}\right)}^3(x-\frac{8}{3})$