Find the point on the graph of $C$ where the slope is $2$.

Question

Let $C$ be the curve with parametric equation $\begin{cases} u(t) = t^2+t \\ v(t) = t^2-t \end{cases}$. Find the point on the graph of $C$ where the slope is $2$.

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So far, I've graphed this and it looks like the point is near the origin, but I don't know how to pinpoint the exact point.

Answer 1

hint

Solve the equation $$\frac {v'(t)}{u'(t)}=2$$

or $$\frac {2t-1}{2t+1}=2$$

which gives $$t=-\frac 32$$