Question

Parameterize the curve of intersection of the surfaces so that the direction is clockwise when viewed from above. Include a sketch of each surface and the curve. x + z = 1 and 2 = 4 - x2 - y2

Answer 1

Answer:

Answer is attached in images

Step-by-step explanation:

Given:

x+z=1 and

$z=4-x^{2} -y^{2}$

Now,

$1-x=4-x^{2} 2-y^{2} 2\\x^{2} -x+y^{2} \\x^{2} -x+1/4+y^{2} =3\\(x-1/2)^{2} +y^{2} =3+1/4\\(x-1/2)^{2} +y^{2} =(\sqrt(13)/2)^{2}$

Which is circle with center (1/2,0) radius

$\sqrt{13/2}$ take, $x=1/2+\sqrt{3} /2 cos\alpha \\y=\sqrt{13}/2 sin\alpha 0\leq \alpha \leq 2\pi$

Now,