10.4 The Hyperbola

Objective: Find the equation, vertices, foci, and asymptotes of hyperbolas.

Standard: Math Analysis 5.0

Definition of a Hyperbola:The set of all points equidistant from ____________________ where the __________ is constant.

Major axis is called the _____________ axis

Standard Equation:

Center:

Vertices:

Foci:

Asymptotes:

Why asymptotes?

Ex. 1) Graph and label the vertices, foci, and asymptotes.

Ex. 2) Find the standard form of the hyperbola with foci at (0, 0) and (8, 0) and vertices at (3, 0) and (5, 0).

Ex. 3) Find the standard form of the hyperbola having vertices at (2, 3) and (2, 9) and asymptotes of slope ±3/2.

Ex. 4) Find the slopes of the asymptotes of the hyperbola given by the equation:

Ex. 5) Find the foci of the hyperbola with the equation:

Assignment:

#28 p. 760#9, 10, 13-16, 22, 23, 27, 28, 45-55 (odd)