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1. The problem statement, all variables and given/known data

Given the following surfaces:

S: z = x^2 + y^2

T: z = 1 - y^2

Find a parametric equation of the curve representing the intersection of S and T.

2. Relevant equations

N/A

3. The attempt at a solution

The intersection will be:

x^2 + y^2 = 1 - y^2

x = (1 - 2y^2)^0.5

At this point, I plug in the following parametrization:

y = sin(t)

Which yields:

x = (1 - 2(sin(t))^2)^0.5

y = sin(t)

z = 1-(sin(t))^2 (from the equation for T)

with t = 0..2*Pi.

Judging from a Maple plot this seems to make sense; the curve is a projected ellipse, but due to the x term I have to split it into two separate segments. I'm pretty sure I should be able to use a more elegant solution with a single curve, but I haven't been able to figure it out - any help would be welcome.

Thanks-

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# Parametric equation of the intersection between surfaces

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