Express the surface x=5cos(theta)sin(phi), y=6sin(theta)sin(phi), z=2cos(phi)?
Express the surface x=5cos(theta)sin(phi), y=6sin(theta)sin(phi), z=2cos(phi) as a level surface f(x,y,z)=3600.
Also, the surface is a ______
A.sphere
B.hyperboloid
C.paraboloid
D.ellipsoid
E.None of these
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Note that (x/5)^2 (y/6)^2 (z/2)^2 = 1 via cos^2(t) sin^2(t) = 1.
==> 144x^2 100y^2 900z^2 = 3600, an ellipsoid.
I hope this helps!
Note that (x/5)^2 + (y/6)^2 + (z/2)^2 = 1, via cos^2(t) + sin^2(t) = 1.
Hence, this is an ellipsoid.
This can be rewritten as follows:
x^2/25 + y^2/36 + z^2/4 = 1
==> 9x^2 + 100y^2 + 900z^2 = 3600.
I hope this helps!