Transcript Hyperbola - Santee Education Complex

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
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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 Ax2 + Bxy + Cy2 + 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 a2 + b2 = c2
 equation of the asymptotes is always:
Graphs of Hyperbolas
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