11a

Section 11.6 / Surfaces in Space

765

\BLE 11.1 Quadric Surfaces

FAlipsoid

(laicuih tl hv Mntluiimlnn

Tracę

Parallcl to .vy-planc Para lici to .tz-piane Parallcl to yz-planc

x² y² z² r/^{2 +} b² + c²

Piane

Ellipsc

The surface is a sphcrc if a = b = c * 0.

yz-trace

Cmi-rnln! In Mdlhcmoliai

Hypcrboloid of One Sheet

r

/>*

•i: i! _ i!

⁺ l,^! c²

Tracę

Piane

Ellipsc Uyperboi a I lyperbola

Parallcl to .ry-piane Parallcl to ,vz-planc Parallcl to yz-piane

The axis of the hypcrboloid corrcsponds to the variable whosc cocfficicnt is negative.

xz-tracc

yz-tracc

Ilyperboloid of Two She. 'v

.    ł    <

Z'    .V"    V"

a² h² Piane

Parallcl to vy-piane Parallcl to vr-piane Parallcl to yz-planc

Tracę

Ellipsc I lyperbola I lyperbola

The axis ol the hypcrlx)loid corrcsponds to the variable whosc cocfficicnt is positivc. Therc is no tracę in the coordinatc piane perpcndicular to this axis.