Math 3D Shapes

Elliptic Paraboloid

• z = 4x² + y²

• stretches along the variable that isn’t squared

• looks like a bowl

Ellipsoid

• x² + y²/9 + z²/4 = 1

• x,y, and z are squared

• all addition

• not equal to 0

• “easy” shape

• looks like a ball

Hyperboloid of one sheet

• x²/4 + y² - z²/4 = 1

• x,y, and z are squared

• 2(+)

• 1(-) —> this is the axis it stretches on

• looks like an hourglass

Cone

• y² = x² + z²/4 —> x² - y² + z²/4 = 0

• 2(+)

• 1(-) —> this is the axis it stretches on

• looks like a cone

Hyperboloid of two sheets

• z²/9 - x² - y²/9 = 1

• 2(-)

• 1(+) —> this is the axis it stretches on

• equal to 1

• x,y,z are squared

• two seperate bowls

Hyperbolic paraboloid

• z = y² - x²

• variable that isn’t squared is the axis it stretches on

• 2(+)

• 1(-)

• looks like a Pringle