ELLIPSOID : traces on the coordinate planes are ellipses 2 2 2 x - - PDF document

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Feb 28, 2024 215 likes •255 views

ELLIPSOID : traces on the coordinate planes are ellipses 2 2 2 x 2 y 2 z 2 = 1 a b c ELLIPTIC PARABOLOID : traces are ellipses and parabolas z = x 2 + y 2 y = x 2 + z 2 HYPERBOLIC PARABOLOID : traces are hyperbolas and parabolas. z =

SLIDE 1

ELLIPSOID: traces on the coordinate planes are ellipses x

2

a

2  y 2

b

2 z 2

c

2=1

ELLIPTIC PARABOLOID: traces are ellipses and parabolas z = x2 + y2 y = x2 + z2

SLIDE 2

HYPERBOLIC PARABOLOID: traces are hyperbolas and parabolas. z = y2 - x2 y = z2 - x2 CONE: Traces are ellipses, hyperbolas and lines. z2 = y2 + x2

SLIDE 3

HYPERBOLOID OF TWO SHEETS: Traces are ellipses and hyperbolas. x2 + y2 - z2 = -1 HYPERBOLOID OF ONE SHEET: Traces are ellipses and hyperbolas. x2 + y2 - z2 = 1