Concept Byte: Graphing Conic Sections

For Use With Lesson 10-1

TECHNOLOGY

You can use your graphing calculator to graph relations that are not functions.

Example

Graph the ellipse x 2 16 + y 2 9 = 1 . fraction x squared , over 16 end fraction , plus , fraction y squared , over 9 end fraction , equals 1 .

• Step 1 Solve the equation for y.

  x 2 16 + y 2 9 = 1 y 2 9 = 1 − x 2 16 y 2 = 9 ( 1 − x 2 16 ) y = ± 3 1 − x 2 16 table with 4 rows and 2 columns , row1 column 1 , fraction x squared , over 16 end fraction , plus , fraction y squared , over 9 end fraction , column 2 equals 1 , row2 column 1 , fraction y squared , over 9 end fraction , column 2 equals 1 minus , fraction x squared , over 16 end fraction , row3 column 1 , y squared , column 2 equals 9 . open . 1 minus , fraction x squared , over 16 end fraction . close , row4 column 1 , y , column 2 equals plus minus 3 . square root of 1 minus , fraction x squared , over 16 end fraction end root , end table

• Step 2 Enter the equations as Y 1 cap y sub 1  and Y 2 . cap y sub 2 , .

  

• Step 3 Select a square window.

  

• Step 4 Graph.

  

Exercises

Graph each conic section.

1. x 2 + y 2 = 25 x squared , plus . y squared , equals 25
2. 4 x 2 + y 2 = 16 4 x squared , plus . y squared , equals 16
3. 9 x 2 − 16 y 2 = 144 9 x squared , minus , 16 y squared , equals 144
4. x 2 − y 2 = 3 x squared , minus . y squared , equals 3
5. x 2 4 − y 2 9 = 1 fraction x squared , over 4 end fraction , minus , fraction y squared , over 9 end fraction , equals 1
6. x 2 + y 2 4 = 16 x squared , plus , fraction y squared , over 4 end fraction , equals 16
7. 1. Graph y = 81 4 − x 2 y equals . square root of 81 over 4 , minus , x squared end root  and y = − 81 4 − x 2 . y equals negative . square root of 81 over 4 , minus , x squared end root . .
   2. Estimate the x-intercepts and find the y-intercepts.
   3. Adjust the window to − 9.3 ≤ x ≤ 9.5 . negative 9.3 less than or equal to x less than or equal to 9.5 .  What are the x-intercepts?
   4. What conic section does the graph represent?

Graph each conic section. Find the x- and y-intercepts.

8. 4 x 2 + y 2 = 25 4 x squared , plus . y squared , equals 25
9. x 2 + y 2 = 30 x squared , plus . y squared , equals 30
10. 9 x 2 − 4 y 2 = 72 9 x squared , minus , 4 y squared , equals 72
11. Writing Explain how to use a graphing calculator to graph x = | y − 3 | . x equals vertical line y minus 3 vertical line .
12. Reasoning Which conic sections can you graph using only one equation? Explain.

Table of Contents