Question

Let C be the curve of intersection of the plane \(x+y+2z=2\) and the paraboloid \(z=x^2+y^2\). Find a parametric equation for the curve C in the form \[r(t)=(x(t),y(t),z(t))\]

Answer 1

no idea where to start. All my examples show just cylinders, so x=cos(t) and y=sin(t). This is also a circle on the x-y plane but the radius is not constant so I am lost