To find the intersection, we need to solve the system of equations:
$z = x^2 + y^2$
$3z = 4 - x^2 - y^2$
Substitute the first equation into the second equation:
$3(x^2 + y^2) = 4 - x^2 - y^2$
Simplify the equation:
$4x^2 + 4y^2 = 4$
Divide by 4:
$x^2 + y^2
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