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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

Sagot :

Answer:

Answer is attached in images

Step-by-step explanation:

Given:

x+z=1 and

[tex]z=4-x^{2} -y^{2}[/tex]

Now,

[tex]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}[/tex]

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

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

Now,

View image VestaHofman
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