Question: Plotting inequalities in 3d

Hi, I have the following problem:

I want to plot the cone given by 1/16*(3x^2+10xz+3z^2-16y^2) and x>=0, z>=0. I tried it with

implicitplot3d([1/16*(3*x^2+10*x*z-16*y^2+3*z^2), x >= 0, z >= 0], x = -5 .. 15, y = -15 .. 15, z = -5 .. 15, grid = [30, 30, 30], style = surface);

But the result is one surface for each inequaility and not the cone.

If i restrict the range of x and z to be 0..15 and dismiss the additonal inequalities, a big part of the cone surface is missing somehow:

Does anybody know how to fix this? Do I have to use another plotcommand?

Thanks for your help!

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