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
x² + y² + z² = 16

what is the shape?
- xy: x² + y² = 16 circle
- xz: x² + z² = 16 circle
- zy: y² + z² = 16 circle
sphere
x2 / 3.3² + y2 / 5.3² + z2 / 3.3² = 1

What is the shape?

Ellipsoid
z = y²What is the shape?

Paraboloid
x² / 16 + y²/16 - z²/4 = 0

What is the shape?

Elliptic Cone
x² / 4 + y² / 9 - z² / 16 = 1

What is the shape?

Hyperboloid of one sheet
z² / 9 - x² / 0 - y² / 25 = 1

What is the shape?

Hyperboloid of 2 sheets
z = x² / 4 + y² / 25

What is the shape?

Elliptic paraboloid
z = x² / 9 - y² / 16

What is the shape?

hyperbolic paraboloid