Problem:

- Find equations of the tangentsto the curve and that pass through the point (4,3).

$\displaystyle \frac{dy}{dx}=\frac{6t^2}{6t}=t$

So the deriviative here is t. When I solve the parametric equations at the point (4,3), I get $\displaystyle t=\pm1$ for the quadratic equation, and t=1 for the cubic equation. The only solution common between them is t=1. So how can there be two tangents through this point? Note that the problemexplicitystates that there are two tangents. I would expect there to be two solutions for t at this point if this were true.