Hyperbolas

Standard Equation of a Hyperbola(Horizontal Transverse Axis)

Example:

Slant asymptotes are at

12

2

2

2

b

y

a

x

xa

by

Standard Equation of a Hyperbola(Vertical Transverse Axis)

Example:

Slant asymptotes are at xb

ay

12

2

2

2

b

x

a

y

Examples

1) Write the standard equation for the hyperbola with vertex (0, 4) and co-vertex (3, 0). Then, sketch the graph.

2) Write the standard equation of a hyperbola with vertex (5, 0) and co-vertex (0, -6). Then, sketch the graph.

3) Sketch the graph of and label the vertices, co-vertices, and foci.

13616

22

xy

4) Find an equation of a hyperbola with vertex (0, 3) and Asymptote y = 3x

• HW

• Pg. 235 (1 – 5odd, 19, 21)