Parametrize the curve of intersections of the surface

Apr 2010
3
0
Parametrize the curve of intersections of the surface - Can someone check my answer?

Parametrize the curve of intersection of the surfaces (a paraboloid and a plane).

z = -x^2 - y^2

y = x


I feel like the answer is

x = t
y = t
z = -t^2 - t^2 = -2t^2

<t, t, -2t^2>

but that doesn't seem right to me for some reason.. if this is incorrect can someone tell me why or show me how..
 
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