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:
“When I think of some of the Persians, the Hindus, the Arabs I knew, when I think of the character they revealed, their grace, their tenderness, their intelligence, their holiness, I spit on the white conquerors of the world, the degenerate British, the pigheaded Germans, the smug self-satisfied French.”
—Henry Miller (1891–1980)