Solution Found!
Quadric surfaces Consider the following
Chapter 12, Problem 38E(choose chapter or problem)
Quadric surfaces Consider the following equations of quadric surfaces.
(a) Find the intercepts with the three coordinate axes, when they exist.
(b) Find the equations of the xy-, xz-, and yz-traces, when they exist.
(c) Sketch a graph of the surface.
Ellipsoids
\(4 x^{2}+y^{2}+\frac{z^{2}}{2}=1\)
Questions & Answers
QUESTION:
Quadric surfaces Consider the following equations of quadric surfaces.
(a) Find the intercepts with the three coordinate axes, when they exist.
(b) Find the equations of the xy-, xz-, and yz-traces, when they exist.
(c) Sketch a graph of the surface.
Ellipsoids
\(4 x^{2}+y^{2}+\frac{z^{2}}{2}=1\)
ANSWER:Solution 38E
Step 1 of 4:
In this problem we need to find the intercepts with the three coordinate axes, the equations of the xy-, xz-, and yz-traces and we have to sketch the graph of the surface.
a. Find the intercepts with the three coordinate axes, when they exist.
Given: Ellipsoids :
First let us rewrite the given equation of ellipsoid into the standard form of the ellipsoid
consider
Now compare the equation with the general equation of the ellipsoid
we get