Answer:
[tex]r(t) = ti + 3t^2 j + (9t^2+36t^4)k[/tex]
Step-by-step explanation:
The two curves are given as
[tex]z= 9x^2 + 4y^2\\y=3x^2[/tex]
We have to find the parametric form for the curve of intersection.
Let us assume that x = t
Then we get
[tex]y = 3x^2 = 3t^2[/tex]
Now
[tex]z=9x^2+4y^2\\= 9t^2+4(3t^2)^2\\= 9t^2+36t^4[/tex]
Hence parametric form would be in vector as
[tex]r(t) = ti + 3t^2 j + (9t^2+36t^4)k[/tex]
