Assignment

Test Unit 8

Review for Final

 
Answers to Review

Unit 8 Conic Sections

This unit focuses on the concept of conic sections.
Most of the graphing in this chapter is easier done by hand.

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Sections 8.1 and 8. 2 Conics and Translation of Conics

Highlights and Objectives

Define Conic Sections
 Parabola - Standard Equation (click here for more information)

Understand the concept of focus point and directrix.

Finding the focus point and directrix

Sketch a parabola centered at the origin or centered at a point (h,k)

Find the equation of a parabola

Ellipse - Standard Equation

Find the major and minor axes. Find   the focal points ( foci), and the vertices

 Sketch an ellipse    centered at the origin or centered at a point (h,k)

Find the equation of an ellipse.

Hyperbola - Standard equation

Find the vertices and foci.
Sketch a hyperbola centered at the origin or centered at a point (h,k)
Find the equation of a hyperbola

Click on the logo to explore hyperbolas online

Comparing Ellipses and Hyperbolas Change any value in the notebook preceded by a square.

Circle - Standard Equation

This is not included in the text in this chapter except briefly on the bottom of page 604. However, it is covered on page 53 of the text. Also note, included on the graphing calculator video is a section on graphing a circle using two functions. This can be used a basis for graphing the ellipse and the hyperbola on the calculator as well. They must be graphed as two separate functions, as they are not functions themselves.

  Use ZSquare to get it to look like a true circle.

Use Completing the Square (Unit 3) to write an equation of a conic in standard form.

             Example1 Circle

x²+ 2x + y² -15 = 0
x²+ 2x + y²       = 15
x²+2x + 1 + y²   = 15+1
(x +1)² +  y²      = 16

This is  the equation of a circle with center (-1,0) with radius 4

Interactive LiveMath Example - circle

          Example 3 - Ellipse

x² + 2x + 4y² -15 = 0
x² + 2x + 4y²       = 15
x² + 2x + 1 + 4y²   = 15+1
(x +1)² + 4y²         = 16   ( divide by  16)
(x +1)² /16 +  y² /4 = 1

This is the equation of an ellipse with center (-1,0).  See page 620 for more information.

Solve simultaneous equations with conics by algebraic and/or graphical methods.

Click on the LiveMath   Logo to explore algebraic methods

Click on the LiveMath   logo to explore  ALL conics

Please make arrangements with the instructor for your final examination.

   

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