Cylinders and Quadric Surfaces

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Homework Statement

Consider the equation below.
x^2 = 3y^2 + 5z^2


Reduce the equation to one of the standard forms.


I believe its surface is a cone, but I'm not sure how to get it into the form

z^2/c^2 = x^2/a^2 + y^2/b^2


thanks!

 

[HallsofIvy]

Your last equation is the standard form for a cone with axis of symmetry along the z axis. Your given equation has axis of symmetry along the x-axis and so cannot be put in exactly that form. It can, of course, be put in the form x^2/a^2= y^2/b^2+ z^2/c^2.