Graph an equation of an ellipse

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Presentation transcript:

Graph an equation of an ellipse 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. 4x2 100 + 25x2 = Divide each side by 100. x2 25 + y24 = 1 Simplify.

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 = 5 and 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, so c = 21 The foci are at ( + 21 , 0), or about ( + 4.6, 0).

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

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

GUIDED PRACTICE for Example 1 STEP 2 Equations. Major Axis Vertices Co - vertices x2 16 + y29 = 1 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, so c = 7 The foci are at ( + 7 , 0).

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

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

GUIDED PRACTICE for Example 1 STEP 2 Equations. Major Axis Vertices Co - vertices x2 36 + y2 49 = 1 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, so c = 13 The foci are at (0 + , 13 ).

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

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

GUIDED PRACTICE for Example 1 STEP 2 Equations. Major Axis Vertices Co - vertices x2 32 + y252 = 1 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 so c = + 4 The foci are at (0, + 4).

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