Appendix C- Part 2Graphs of Second Degree

Equations

Today, we will review 2nd Degree equations such as:

Today, we will review 2nd Degree equations such as:

Today, we will review 2nd Degree equations such as:

Ellipse

Today, we will review 2nd Degree equations such as:

Today, we will review 2nd Degree equations such as:

Hyperbola

Ellipse:

Ellipse:

Ellipse:

If the equation can be placed in this form, then:

Ellipse:

If the equation can be placed in this form, then:

Ellipse:

If the equation can be placed in this form, then:

Ellipse:

If the equation can be placed in this form, then:

Example:

Example:

Example:

Discussion:

Discussion:

• Which axis is the major axis?

Discussion:

• Which axis is the major axis?

• Length of the major axis is always?

Hyperbola:

Hyperbola:

Hyperbola:

Hyperbola:

Example:

Example:

List equation of the asymptotes:

Rectangular Hyperbola:

Rectangular Hyperbola:

Rectangular Hyperbola:

If k is a positive value, then the curve

lies in quadrants 1 and 3.

Rectangular Hyperbola:

If k is a negative value, then the curve

lies in quadrants 2 and 4.

Rectangular Hyperbola:

All curves of this type have asymptotes with

equations: x = 0 and y = 0

Recognize shifted conics:

Recognize shifted conics:

Recognize shifted rectangular Hyperbola:

Recognize shifted rectangular Hyperbola:

Example:

Find equations of both asymptotes:

Assignment:

Page A 2313-31 odd, 35 Make sketches for 13 – 21 odd and for the rest just identify the type of curve (hyperbola, ellipse, circle, or parabola).