A line $t$ passes through the point $A(-3, 0)$ and is tangent to the parabola with equation $\lambda: x=3y^2$ at point $P$. What is the equation of line $t$?
Well, I could try using the equation for a line $t:y=mx+n$, and substitute its equation into the parabola equation, calculating the determinant and finding the slope. However, I would like to solve this problem using the vector approach of Analytic Geometry, that is, if $t \cap \lambda = P(a, b)$, then the parametric equation of the line will be given by $$t: \begin{cases} x= -3 + (a+3)t \\ y=0+bt\end{cases}$$