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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.

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EXAMPLE 1

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  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.

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