Finding tangent's equation that touchs parabola at $(4, 4)$

Question

$y^2 = 4x$ is equation of a parabola. What is the equation of the tangent which touchs parabola at $(4,4)$ ? I don't know how to solve it, please help.

(Excuse my bad grammer. Hope you understand what I mean)

Answer 1

If you don't know about derivatives, you can find the slope solving the system $$\left\{\begin{array}{l}y^2=4x\\y-4=m(x-4)\end{array}\right.$$

If you solve it for $x$, the discriminant will be an expression on $m$, which should be $0$, since the line and the parabola have only one common point.