Find a vector function that represents the curve of intersection of the paraboloid z=4x2+3y2

Question

and the cylinder y=5x2
. Use the variable t for the parameter.
r(t)=

Answer 1

To find the curve of intersection between the paraboloid and the cylinder, we need to find the values of x, y, and z that satisfy both equations.

First, let's substitute y=5x^2 into the equation of the paraboloid:

z = 4x^2 + 3(5x^2)
z = 4x^2 + 15x^2
z = 19x^2

Now, let's express x and z in terms of the parameter t:

x = t
z = 19t^2

To find y, substitute x=t into the equation of the cylinder:

y = 5(t^2)

So, the vector function that represents the curve of intersection is:
r(t) = <t, 5t^2, 19t^2>