Hyperbolas 9.3. Definition of a Hyperbola A hyperbola is the set of all points (x, y) in a plane, the difference of whose distances from two distinct.

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Presentation transcript:

Hyperbolas 9.3

Definition of a Hyperbola A hyperbola is the set of all points (x, y) in a plane, the difference of whose distances from two distinct fixed points (foci) is a positive constant.

Standard Form Equation of a Hyperbola The standard form of the equation of a hyperbola with center at (h, k) is Horizontal Vertical The vertices are a units from the center, and the foci are c units from the center. c 2 = a 2 + b 2.

Example 1 Find the standard form of the equation of the hyperbola with foci (-1, 2) and (5, 2) and vertices (0, 2) and (4, 2).

Example 2 Sketch the hyperbola whose equation is 4x 2 – y 2 = 16.

Example 3 Find the standard form of the equation of 9x 2 – y 2 – 36x – 6y + 18 = 0.