$y^2 = 4x$ 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)
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Implicit derivation give us $\frac{dy}{dx}=\frac{2}{y}$ near of $(4,4)$, then the slope of the tangent line you are looking for is $m_{\text{tangent}}=\frac{2}{4}=\frac{1}{2}$. – Ángel Mario Gallegos Apr 14 '15 at 05:01
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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.
ajotatxe
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