11.6
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How do you find the trace for a shape?
set one variable to zero and get the equation containing the other 2.

What contains 2 ellipses and a circle?
an ellipsoid

What contains 2 lines and a parabola?
A paraboloid

what contains 3 circles?
a sphere

What contains 2 criss crosses and a point
elliptic cone

What contains an ellipse and 2 hyperbolas?
hyperboloid of one sheet

Give an example of a hyperboloid of one sheet
a nuclear power plant

What is the relationship of an elliptic cone as the z increases?
The radius begins to expand

What contains no trace and 2 hyperbolas?
a hyperboloid of two sheets

what contains a point, parabola and hyperbola?
elliptic paraboloid

What contains a point, parabola and upside down parabola?
hyperbolic paraboloid

x + 3y + z = 4
 xy: x +3y = 4
 xz: x +z = 4
 zy: 3y + z = 4

x^{2} + y^{2} + z^{2} = 16
what is the shape?
 xy: x^{2} + y^{2} = 16 circle
 xz: x^{2} + z^{2} = 16 circle
 zy: y^{2} + z^{2} = 16 circle
sphere

x2 / 3.3^{2} + y2 / 5.3^{2} + z2 / 3.3^{2} = 1
What is the shape?
Ellipsoid

z = y^{2
}What is the shape?
Paraboloid

x^{2} / 16 + y^{2}/16  z^{2}/4 = 0
What is the shape?
Elliptic Cone

x^{2} / 4 + y^{2} / 9  z^{2} / 16 = 1
What is the shape?
Hyperboloid of one sheet

z^{2} / 9  x^{2} / 0  y^{2} / 25 = 1
What is the shape?
Hyperboloid of 2 sheets

z = x^{2} / 4 + y^{2} / 25
What is the shape?
Elliptic paraboloid

z = x^{2} / 9  y^{2} / 16
What is the shape?
hyperbolic paraboloid
