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re12
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Homework Statement
Parametrize the intersection of
the paraboloid z = x2 + y2
and the plane 3x -7y + z = 4
between 0 [tex]\leq[/tex] t [tex]\geq[/tex] 2*pi
When t = 0, x will be greatest on the curve.
Homework Equations
The Attempt at a Solution
I never really know how to do these kinds of problem. I am more familiar with parametrizing straight lines. Here is what I have done so far
I substitute the z in the plane equation with the paraboloid
3x - 7y + x2 + y2 = 4
x2 + 3x + (3/2)2 + y2 -7y + (7/2)2 = 37/2
(x + 3/2) 2 + (y - 7/2)2 = 37/2
which is a circle centered at (-3/2 , 7/2) with radius 37/2
So to parametrize x, I did
x = [tex]\sqrt{37/2}[/tex] - (3/2) at t = 0 so
x = ([tex]\sqrt{37/2}[/tex] - 3/2) * cos(t)
This may be wrong, but I am not sure. Please let me know if I am on the right track and how can I continue with this problem. The y and z components seem to be more complicated.
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