10.5 Hyperbolas Algebra 2.

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Presentation transcript:

10.5 Hyperbolas Algebra 2

Definitions Hyperbola- The set of all points P such that the difference of the distances from P to two fixed points, called the foci. Vertices-The intersection of the line that contains the foci and the hyperbola Transverse Axis- The line segment joining the vertices Center- The middle of the hyperbola

Diagram of a Hyperbola

Characteristics of a Hyperbola (Centerd at the Origin) The standard form of the equation of a hyperbola with center at (0, 0) is as follows… Equation Transverse Axis Asymptotes Vertices

Examples: Write the equation in standard form. Identify vertices, foci, and asymptotes. 16x2 – 9y2 = 144 100x2 – 49y2 – 4900 = 0 y2 – 25x2 = 25

Examples: Draw the hyperbola given by 9x2 – 16y2 = 144 Draw the hyperbola given by 9y2 – 16x2 = 144

Examples: Write an equationof the hyperbola with foci at (0, -5) and (0, 5) and vertices at (0, -3) and (0, 3). Write an equation of the hyperbola with foci (-2, 0) and (2, 0) and vertices at (-1, 0) and (1, 0).