By: Leonardo Ramirez Pre Calculus Per.6 Mr. Caballero

Hyperbola

What is a Hyperbola? The term hyperbola was introduced by the Greek mathematician Apollonius of Perga as well as the terms Parabola, and Ellipse. In the world of Mathematics a Hyperbola is a smooth planar curve having two connected components of branches. The hyperbola is traditionally described as one of the kinds of conic section or intersection of a plane and a cone. A hyperbola is the set of all points such that the difference of the distances between any point on the hyperbola and two fixed points is constant. The Hyperbola has two focal points called foci. A hyperbola is an open curve, meaning that it continues indefinitely to infinity, rather than closing on itself as an ellipse does.

Conic sections A hyperbola may be defined as the curve of intersection between a right circular conical Surface and a plane that cuts through both halves of the cone.

Facts about Hyperbola The Graph of a Hyperbola is not continuous. Every hyperbola has two distinct branches. The line segment containing both foci of a hyperbola whose endpoints are both on the hyperbola is called the transverse axis. The foci lie on the transverse axis and their midpoint is called the center. The Hyperbolas look somewhat like a letter X The Hyperbolas has a traverse axis: this is the axis on which the two foci are. The hyperbola also has asymptotes this are two lines that the hyperbola s come closer and closer to touch but do not really touch.

Equation of Hyperbolas On a Cartisian plane a hyperbola is define by the equation Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 where all of the coefficients are real, and where more than one solution, defining a pair of points (x, y) on the hyperbola, exists. hyperbola centered at (h,k): The equation of a hyperbola is written as:

To determine the foci of a hyperbola you use the Formula a 2 + b 2 = c 2 equation of the asymptotes is always:

Graphs of Hyperbolas

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