Concept
Degenerate conic
The solution set of a quadratic that is a point, a line, a pair of lines or nothing at all rather than a curve. These are the sections of a cone by planes through its apex, and the discriminant names their type while a second determinant detects the degeneracy.
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
One cone, four curves
The circle, the ellipse, the parabola and the hyperbola look like four separate objects with four separate equations. They are one object, cut at four angles.
One sign decides which curve
The general quadratic in two variables has six coefficients and draws a conic. Which of the four it draws is settled by a single combination of three of them, and the other three cannot change the answer however they are chosen.
Named alongside it
The objects these essays reach for when they reach for this one.
ConicEllipseHyperbolaParabolaDandelin spheresDiscriminantEigenvalueFocusProjectionQuadratic form