Finding Tangent line from Parametric I need to find an equation of the tangent line to the curve $x=5+t^2-t$, $y=t^2+5$ at the point $(5,6)$.
Setting $x=5$ and $y = 6$ and solving for $t$ gives me $t=0,1,-1$. I know I have to do y/x, and then take the derivative. But how do I know what $t$ value to use?

You have 
i) $x=5+t^2-t$ and ii) $y=t^2+5$ and $P=(5,6)$.
From $P=(5,6)$ you get $x=5$ and $y=6$.
From ii) you get now $t^2=1\Rightarrow t=1$ or $t=-1$ and from i) you get (knowing that $t\in${1,-1} ):$\ $ $t=1$
Your curve has the parametric representation
$\gamma: I\subseteq\mathbb{R}\rightarrow {\mathbb{R}}^2: t\mapsto (5+t^2-t,t^2+5)$.
Therefore, $\frac{d}{dt}\gamma=(2t-1,2t)$.
Put  $t=1$ into the derivative of $\gamma$ and from this you can get the slope of the tangent in P.
