1. 10.5 Hyperbolas
Algebra 2

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

3. Diagram of a Hyperbola

4. 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

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

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

7. 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).