Appendix C- Part 2 Graphs of Second Degree Equations

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

Ellipse

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

Hyperbola

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:

Discussion:

Which axis is the major axis?

Discussion: Which axis is the major axis? Length of the major axis is always?

Hyperbola:

Example:

List equation of the asymptotes:

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 rectangular Hyperbola:

Example: Find equations of both asymptotes:

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