(Solved): Identify the following surfaces as an elliptical paraboloid, hyperbolic paraboloid, a hyperboloid ...

Identify the following surfaces as an elliptical paraboloid, hyperbolic paraboloid, a hyperboloid of one sheet, a hyperboloid of two sheets, a cone, a circular cylinder, an elliptical cylinder, or a parabolic cylinder, and identify the axis of symmetry as the x-axis, the yaxis, or the z-axis. a. \[ -5 x^{2}+5 y^{2}-z^{2}=0 \] b. \[ -7 x^{2}-2 y^{2}+z^{2}=1 \] c. \[ 5 y^{2}-3 x^{2}-7 z^{2}+1=0 \] d. \[ 3 y^{2}+3 z^{2}=1 \] e. \[ 3 x^{2}+4 y^{2}-z=0 \]