Consider the following surface:
x = 4y^2 + 4z^2
What's this surface called?
What coordinate plane does z=0 define?
What's the trace of this surface in the xz plane look like?
What's the trace of this surface in the planes x=k look like?
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Consider the following surface:
x = 4y^2 + 4z^2
What's this surface called?
What coordinate plane does z=0 define?
What's the trace of this surface in the xz plane look like?
What's the trace of this surface in the planes x=k look like?
Hello, Ideasman!
I use the standard orientation of the three coordinate axes.Code:z




*       y
/
/
/
x
It is a paraboloid.Quote:
Consider the following surface: .
What's this surface called?
is the plane (the "floor" of the graph).Quote:
What coordinate plane does define?
The plane is the "left wall" of the graph.Quote:
What's the trace of this surface in the plane look like?
Let and we have: .
This is a parabola on the "left wall", vertex at the origin,
. . opening in the positive direction.
Quote:
What's the trace of this surface in the planes look like?
Let . .We have: .
These are circles: centered on the axis with radius