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Discriminant - Discriminant of a conic section | | Discriminant - Discriminant of a conic section: Encyclopedia II - Discriminant - Discriminant of a conic section | | For a conic section defined by the real polynomial:
ax2 + bxy + cy2 + cx + ey + f= 0,
the discriminant is equal to
b2 − 4ac,
and determines the shape of the conic section. If the discriminant is less than 0, the equation is of an ellipse or a circle. If the discriminant equals 0, the equation is that of a parabola. If the discriminant is greater than 0, the equation is that of a hyperbola. This formula will ...
See also:Discriminant, Discriminant - Discriminant of a polynomial, Discriminant - Discriminant of a conic section, Discriminant - Discriminant of a quadratic form, Discriminant - Discriminant of an algebraic number field | | | Discriminant, Discriminant - Discriminant of a conic section, Discriminant - Discriminant of a polynomial, Discriminant - Discriminant of a quadratic form, Discriminant - Discriminant of an algebraic number field | | |
| | | Discriminant: Encyclopedia II - Discriminant - Discriminant of a conic section
Discriminant - Discriminant of a conic section
For a conic section defined by the real polynomial:
ax2 + bxy + cy2 + cx + ey + f= 0,
the discriminant is equal to
b2 − 4ac,
and determines the shape of the conic section. If the discriminant is less than 0, the equation is of an ellipse or a circle. If the discriminant equals 0, the equation is that of a parabola. If the discriminant is greater than 0, the equation is that of a hyperbola. This formula will not work for degenerate cases (when the polynomial factorises).
Other related archivesAlgebraic number theory, Conic sections, Discriminant of an algebraic number field, Polynomials, Quadratic forms, algebraic number fields, algebraic number theory, algebraic structures, characteristic, circle, coefficients, complex, conic section, determinant, ellipse, field, fields, hyperbola, mathematics, parabola, polynomial, polynomials, quadratic forms, quadratic formula for the roots, quadratic polynomial, ramification, real, resultant, shape, splitting field, square root, symmetric matrix, up to
 Adapted from the Wikipedia article "Discriminant of a conic section", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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