Graph and Write Equations of Hyperbolas

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Graph and Write Equations of Hyperbolas Section 9.5 Graph and Write Equations of Hyperbolas

California Standard: 16.0: Students demonstrate and explain how the geometry of the graph of a conic section depends on the coefficients of the quadratic equation representing it.

By following instructions, students will be able to: OBJECTIVE(S): By following instructions, students will be able to: Graph and write equations of hyperbolas.

Def: A hyperbola is the set of all points P in a plane such that the sum of the distances between P and two fixed points, called the foci, is a constant. Standard Equation of a Hyperbola with Center at the Origin y y x x

EXAMPLE 1: Graph . Identify the vertices, foci, and asymptotes of the hyperbola.

EXAMPLE 2: Write an equation of the hyperbola with foci at (-4,0), and (4,0) and vertices at (-3,0) and (3,0). 6

U-TRY#1: Graph the equation. Identify the vertices, foci, and asymptotes of the hyperbola. A) B) C) Write an equation of the hyperbola with the given foci and vertices Foci (-3,0), (3,0); vertices (-1,0) and (1,0) Foci (0,-10), (0,10); vertices (0,-6) and (0,6)

HOMEWORK Sec 9.5 WS