# 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:

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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

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