Objective 9.1- Conic Sections

Objective 9.1- Conic Sections

A. Circles

· Standard Form: ______

o Center: ______

o Radius: ______

· General Form: ______

Example 1: Write the standard form of the equation of the circle that is tangent to the y-axis and

has its center at (-5, -4).

Example 2: Write the standard form of the equation of the circle: . Then identify the center and radius.

B. Ellipses

Horizontal Major Axis / Vertical Major Axis
Standard Form
General Form

Example 1: For the equation identify the center and the direction of the major axis.

Example 2: Rewrite the equation of the following ellipse in standard form. Then identify the center and the direction of the major axis.

C. Hyperbolas

Horizontal Transverse Axis / Vertical Transverse Axis
Standard Form
General Form

Example 1: For the equation identify the center and the direction of the transverse axis.

Example 2: Rewrite the equation of the following hyperbola in standard form. Then identify the center and the direction of the transverse axis.

E. Parabolas

Vertical AOS / Horizontal AOS
Standard Form
General Form

Example 1: Rewrite the equation in standard form. Then tell the direction of the AOS and the vertex.

Example 2: Rewrite the equation in standard form. Then tell the direction of the AOS and the vertex.

1) Complete the square:

2) Complete the square:

3) Write the equation of a circle in standard form that has a radius of 3 and center (-2, 1)

4) Write the equation of the following circle in standard form. Then identify the center and radius.

5) For the equation identify the center and the direction of the major axis.

6) Rewrite the equation of the following ellipse in standard form. Then identify the center and the direction of the major axis.

7) Rewrite the equation of the following hyperbola in standard form. Then identify the center and the direction of the transverse axis:

1) Complete the square:

2) Complete the square:

3) Write the equation of a circle in standard form that has a radius of 3 and center (-2, 1)

4) Write the equation of the following circle in standard form. Then identify the center and radius.

5) For the equation identify the center and the direction of the major axis.

6) Rewrite the equation of the following ellipse in standard form. Then identify the center and the direction of the major axis.

7) Rewrite the equation of the following hyperbola in standard form. Then identify the center and the direction of the transverse axis:

F. Classifying Conics

· If given an equation in general form: Get all terms on one side!

Hints:

Circle –

Ellipse –

Hyperbola –

Parabola –

Classify the following conics: