Quadric Surfaces Flashcards
1
Q
A
Horizontal traces in z = k are ellipses if k > c or k < - c.
Vertical traces are hyperbolas.
The two minus signs indicate the two sheets.
2
Q
A
Horizontal traces are ellipses.
Vertical traces in the planes x=k and y=k are hyperbolas if k != 0 but are pairs of lines if k = 0.
3
Q
A
Horizontal traces are ellipses.
Vertical traces are parabolas.
The variable raised to the first power indicates the axis of the parabaloid.
4
Q
A
Horizontal traces are ellipses.
Vertical traces are hyperbolas.
The axis of symmetry corresponds to the variable with a negative coefficient.
5
Q
A
All traces are ellipses.
If a=b=c, the ellipsoid is a sphere.
6
Q
A
Horizontal traces are hyperbolas.
Vertical traces are parabolas.
The case where c < 0 is illustrated.
