Sketch the space curve represented by the intersection of the surfaces. Then represent the curve by a vector-valued function using the given parameter.
z = x^2 + y^2, x + y = 0, x = t
The Attempt at a Solution
Space curve sketched (elliptic paraboloid corresponding to z-axis)
Vector valued function: x = t, y = -t; z = t^2 + (-t)2; z = 2t^2; r(t) = ti - tj + 2t^2k
**Intersection of the surface, not sure how to obtain this. I have the feeling once I get it I'm gonna be shaking my head for having forgotten something. So I've tried setting
x^2 + y^2 = x + y
tried substituting in t for x and y values
tried reverse engineering what I'm supposed to do with the answers plugged in to the equations.
tried finding x int, y int, and z int.
Just don't know how to procede. Any assistance is greatly appreciated.