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1-Consider the equation below. 16x2 + y2 + 16z2 %u2212 8y %u2212160z + 400 = 0 Reduce the equation to one of the standardforms.
Classify the surface.
elliptic cylinder
elliptic paraboloid
ellipsoid
circular cone
hyperboloid of two sheets
parabolic cylinde
r hyperboloid of one sheet
hyperbolic paraboloid
Consider the equation below.
reduce the equation to one of the standard forms.
1. Reduce the equation to one of the standard forms.
2. Classify the surface. (ellipsoid, elliptic paraboloid, hyperbolic paraboloid, cone, hyperboloid of one sheet, hyperboloid of two sheets)
1. Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is 3 times the distance from P to the yz-plane. 2. Identify the surface.
parabolic cylinder
cone
hyperboloid of one sheet