1 / 12

EXAMPLE 1

100. x 2. 4 x 2. 25 x 2. 100. 25. 100. 100. =. +. y 2 4. +. = 1. EXAMPLE 1. Graph an equation of an ellipse. Graph the equation 4 x 2 + 25 y 2 = 100 . Identify the vertices, co-vertices, and foci of the ellipse. SOLUTION. STEP 1.

darryl
Download Presentation

EXAMPLE 1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 100 x2 4x2 25x2 100 25 100 100 = + y24 + = 1 EXAMPLE 1 Graph an equation of an ellipse Graph the equation 4x2 + 25y2 = 100. Identify the vertices, co-vertices, and foci of the ellipse. SOLUTION STEP 1 Rewrite the equation in standard form. 4x2 + 25y2 = 100 Write original equation. Divide each side by 100. Simplify.

  2. soc = 21 The foci are at( + 21 , 0),or about ( + 4.6, 0). EXAMPLE 1 Graph an equation of an ellipse STEP 2 Identify the vertices, co-vertices, and foci. Note that a2 = 25 and b2 = 4, so a = 5and b = 2. The denominator of the x2 - term is greater than that of the y2 - term, so the major axis is horizontal. The vertices of the ellipse are at (+a, 0) = (+5, 0). The co-vertices are at (0, +b) = (0, +2). Find the foci. c2= a2– b2= 52– 22= 21,

  3. EXAMPLE 1 Graph an equation of an ellipse STEP 3 Draw the ellipse that passes through each vertex and co-vertex.

  4. + x2 x2 16 16 + = 1 y29 y29 for Example 1 GUIDED PRACTICE Graph the equation. Identify the vertices, co-vertices, and foci of the ellipse. 1. = 1 SOLUTION STEP 1 The equation is in standard form.

  5. + = 1 x2 16 soc = The foci are at( + 7 , 0). y29 7 for Example 1 GUIDED PRACTICE STEP 2 Equations. Major Axis Vertices Co - vertices Horizontal + 4, 0 0, + 3 The vertices of the ellipse are at (+ 4, 0) and co-vertices are at (0, + 3). Find the foci. c2 = a2– b2 = 42– 32 = 7,

  6. for Example 1 GUIDED PRACTICE STEP 3 Draw the ellipse that passes through each vertex and co-vertex.

  7. y2 49 y2 49 x2 x2 + + 36 36 = 1 for Example 1 GUIDED PRACTICE 2. = 1 SOLUTION STEP 1 The equation is in standard form.

  8. y2 49 x2 + 36 = 1 soc = The foci are at(0 + , 13 ). 13 for Example 1 GUIDED PRACTICE STEP 2 Equations. Major Axis Vertices Co - vertices Vertical 0, + 7 + 6, 0 The vertices of the ellipse are at (0, + 7) and co-vertices are at (+ 6, 0). Find the foci. c2 = a2– b2 = y2– 62 = 13,

  9. for Example 1 GUIDED PRACTICE STEP 3 Draw the ellipse that passes through each vertex and co-vertex.

  10. 25x2 x2 9y2 1 = + 225 9 225 y225 + = 1 for Example 1 GUIDED PRACTICE 3. 25x2 + 9y2 = 225 SOLUTION STEP 1 Rewrite the equation in standard form. 25x2 + 9y2 = 225 Write original equation. Divide each side by 225. Simplify.

  11. + = 1 x2 32 soc = + 4 y252 for Example 1 GUIDED PRACTICE STEP 2 Equations. Major Axis Vertices Co - vertices Vertical (0 + 5), + 3, 0 The vertices of the ellipse are at (0 + 5), and co-vertices are at (+ 3, 0). Find the foci. c2 = a2– b2 = 25– 9 = 16 The foci are at(0, + 4).

  12. for Example 1 GUIDED PRACTICE STEP 3 Draw the ellipse that passes through each vertex and co-vertex.

More Related