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WZ
Numerade Educator

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Problem 47 Hard Difficulty

Try to sketch by hand the curve of intersection of the circular cylinder $ x^2 + y^2 = 4 $ and the parabolic cylinder $ z = x^2 $. Then find parametric equations for this curve and use these equations and a computer to graph the curve.

Answer

$x=2 \cos t, y=2 \sin t, z=4 \cos ^{2} t, \quad 0 \leq t \leq 2 \pi$

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Video Transcript

the problem is try to sketch the hand. The curve of intersection of the circular Salinger X squared plus y squared is secret war, and there's a parabolic sine you Z is equal to X squared. Then find a parametric equations for this curve and the youth fifty equations and a computer to graph the craft. First, let's sketch a hand. It's a curse First John graph After circular assigned er that would choose some points on the curse of intersection over the sun. Circular Senator Andi is a pair of all excited We can choose, you know, two zero zero negative to zero Teo Theo two and two zero Negative too. So the point. They're a truth. Zero point. They're addicted to it all. Zero to Hey, is this negative? Two zero two negative. Two zero two point then that's job. A curve of intersection after secret Sander Andi is a Powerball expanded. It's like like this. Then be used, some graphing, the wise to graph the kerf. This's the graph ofthe curve. Yeah, we use the parametric equations actually go to to assign him. Why is because to sign he and C because you war call sign. He's scored three years Parametric equations. Then we can draw the graph