CHAPTER III: CONICS AND QUADRICS - OCW UPM
CHAPTER III: CONICS AND QUADRICS - OCW UPM
CHAPTER III: CONICS AND QUADRICS - OCW UPM
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AFFINE <strong>AND</strong> PROJECTIVE GEOMETRY, E. Rosado & S.L. Rueda<br />
then Q ∩ π ∞ is a conic of the plane at infinity π ∞ with matrix<br />
⎛<br />
⎞<br />
a 11 a 12 a 13<br />
A 00 = ⎝ a 12 a 22 a 23<br />
⎠ .<br />
a 13 a 23 a 33<br />
Proposition. The quadric Q has a center if and only if det A 00 ≠ 0. Besides,<br />
If det A 00 ≠ 0, then the conic Q ∩ π ∞ is regular and Q has a center.<br />
If det A 00 = 0, then the conic Q ∩ π ∞ is degenerate and Q has no center.
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