Question

Find a vector function that represents the curve of intersection of the paraboloid z= 9x^2 + 4y^2 and the cylinder y=3x^2. Use the variable t for the parameter.
r(t)=

Answer 1

Answer:

$r(t) = ti + 3t^2 j + (9t^2+36t^4)k$

Step-by-step explanation:

The two curves are given as

$z= 9x^2 + 4y^2\\y=3x^2$

We have to find the parametric form for the curve of intersection.

Let us assume that x = t

Then we get

$y = 3x^2 = 3t^2$

Now

$z=9x^2+4y^2\\= 9t^2+4(3t^2)^2\\= 9t^2+36t^4$

Hence parametric form would be in vector as

$r(t) = ti + 3t^2 j + (9t^2+36t^4)k$