How does this surface looks like? The formula is $({x^4 \over{a^4}} + {y^2 \over{b^2}} + {z^2 \over{c^2}})^2 = {x^2 \over{p^2}}$, where $a,b,c,p$ is positive. The left part is pretty similuar to ellipsoid, but there are few differences. I also have tried to use the difference of two squares and brackets expansion, but it didn't help. 
And the second function - what is the volume of this body?
Thanks for any help!

After anisotropic scaling you can consider the reduced equation
$$(x^4+y^2+z^2)=x^2.$$
It is symmetric by revolution and its section by the plane $z=0$, $$(x^4+y^2)^2=x^2,$$
or
$$y=\pm\sqrt{|x|-x^4}.$$
The study is not very difficult.

So the surface is an hourglass stretched along the three axis.
The volume is given by the integral of the area of the cross section by the $yz$ plane, $\pi y^2=|x|-x^4$ over the whole $x$ range; then apply the scaling factors.
