In mathematics, a degenerate conic is a conic (degree-2 plane curve, the zeros of a degree-2 polynomial equation, a quadratic) that fails to be an irreducible curve. This can happen in two ways: either it is a reducible variety, meaning that its defining quadratic factors as the product of two linear polynomials (degree 1), or the polynomial is irreducible but does not define a curve, but instead a lower-dimension variety (a point or the empty set); this latter can only occur over a field that is not algebraically closed, such as the real numbers.
Read more about Degenerate Conic: Examples, Classification, Discriminant, Applications, Degeneration, Points To Define, Degenerate Ellipse With Semiminor Axis of Zero
Famous quotes containing the word degenerate:
“It would seem as if the very language of our parlors would lose all its nerve and degenerate into palaver wholly, our lives pass at such remoteness from its symbols, and its metaphors and tropes are necessarily so far fetched.”
—Henry David Thoreau (1817–1862)