Try to sketch by hand the curve of intersection of the parabolic cylinder y = x2 and the top half of the ellipsoid x2 + 5y2 + 5z2 = 25. Then find

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Try to sketch by hand the curve of intersection of the parabolic cylinder y = x² and the top half of the ellipsoid x² + 5y² + 5z² = 25. Then find parametric equations for this curve.
(x(t), y(t), z(t)) = (
√5-2²-A
Use these equations and a computer to graph the curve.
2
1-
OB
Z 0-
-13
-0.5
X
Z
2
1.5-
1
0.5
0.2
16-
14
12
10
z 8
6
4
2
0
0.4
0.6
y 0.8
3
1.2
0.80.60.40.20
2
1.5-
Z
11
0.5
0
0.5
y
y
0
1
0.5
1.5
1 1
2
1.5
0.5
X
90.604020
0
-0.4
-0.2
X
-1
-0.5
-1.5
Transcribed Image Text:Try to sketch by hand the curve of intersection of the parabolic cylinder y = x² and the top half of the ellipsoid x² + 5y² + 5z² = 25. Then find parametric equations for this curve. (x(t), y(t), z(t)) = ( √5-2²-A Use these equations and a computer to graph the curve. 2 1- OB Z 0- -13 -0.5 X Z 2 1.5- 1 0.5 0.2 16- 14 12 10 z 8 6 4 2 0 0.4 0.6 y 0.8 3 1.2 0.80.60.40.20 2 1.5- Z 11 0.5 0 0.5 y y 0 1 0.5 1.5 1 1 2 1.5 0.5 X 90.604020 0 -0.4 -0.2 X -1 -0.5 -1.5
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