# Transcribed Image Text: Consider the surfaces z = x² + y², z + 2x + 2y = 0 ot) Find the projection of the curve of intersection on the ry-plane (nt:

Excerpt
a parametric equation for the curve of intersection of the two surfaces and compute the curvature at 0 = 0 (nt: Don’t forget about the z-direction, the parametrization in part (b) is the projection to the ry-plane). Proble m 2 (15nt) Consider the f nation

Transcribed Image Text: Consider the surfaces
z = x² + y², z + 2x + 2y = 0
ot) Find the projection of the curve of intersection on the ry-plane (nt: Just use the two equations to get
a relation involving x and y only)
-) Find a parametric equation describing the projected curve of intersection in part (a) (nt: Use polar
coordinates to solve for r in terms of 0. Then find x and y in terms of 0 only.)
pt) Find a parametric equation for the curve of intersection of the two surfaces and compute the curvature
at 0 = 0 (nt: Don’t forget about the z-direction, the parametrization in part (b) is the projection to the
ry-plane).
Proble m 2
(15nt) Consider the f nation