Question

Find a vector function that represents the curve of intersection of the two surfaces: z=4x^2 + y^2 and y=x^2

Answer 1

Anybody?

Answer 2

Find a Cartesian equation for the intersection first:
Plugging y=x^2 into the equation for z, we have
\[z=4x^2+(x^2)^2=4x^2+x^4\]
Thus, if you let x=t, then a vector equation for the intersection is:
\[\mathbf{r}(t)=\left<t, t^2, 4t^2+t^4\right>\]