📂Geometry

Hyperbola

Definition ¹

The set of points on a plane whose difference in distances to two distinct points $F$, $F^{\prime}$ is constant is called a hyperbola.

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• The points $F$, $F^{\prime}$ are called focus.
• The midpoint of segment $\overline{FF^{\prime}}$ is called center.
• The two points where the hyperbola intersects segment $\overline{FF^{\prime}}$, $A$, $A^{\prime}$, are called vertices.
• The segment $\overline{AA^{\prime}}$ is called major axis.

Description

Method of Discrimination

For a given quadratic curve $Ax^{2} + Bxy + Cy^{2} + Dx + Ey + F = 0$, $\Delta = B^{2} - 4AC$ is called the discriminant. A quadratic curve is a hyperbola if the discriminant is positive.