**1. The problem statement, all variables and given/known data**
Parametrize the intersection of

the paraboloid z = x

^{2} + y

^{2}
and the plane 3x -7y + z = 4

between 0

t

2*pi

When t = 0, x will be greatest on the curve.

**2. Relevant equations**
**3. The attempt at a solution**
I never really know how to do these kinds of problem. I am more familiar with parametrizing straight lines. Here is what I have done so far

I substitute the z in the plane equation with the paraboloid

3x - 7y + x

^{2} + y

^{2} = 4

x

^{2} + 3x + (3/2)

^{2} + y

^{2} -7y + (7/2)

^{2} = 37/2

(x + 3/2)

^{2} + (y - 7/2)

^{2} = 37/2

which is a

circle centered at (-3/2 , 7/2) with radius 37/2

So to parametrize x, I did

x =

- (3/2) at t = 0 so

x = (

- 3/2) * cos(t)

This may be wrong, but I am not sure. Please let me know if I am on the right track and how can I continue with this problem. The y and z components seem to be more complicated.