fector function of the curve of intersection

[maeveoneill]

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

I read an example and it just started off by subbing x=t. and using it to find values for y and z that could then just be simply subbed into the vector equation.
Is that correct?

Also, what would this look like??? What shape would the curve of intersection be?

 

[maeveoneill]

oh also, those equations x = h + r cost t, y = h + r sin t... is that only for cirlces???