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Your Notes
Example 1 Graph an equation of an ellipse
Graph the equation 9x2 1 36y2 5 324. Identify the
vertices, co-vertices, and foci of the ellipse.
1. Rewrite the equation in standard form.
9x2 1 36y2 5 324 Write original equation.
1 5 Divide each side by .
1 5 1 Simplify.
2. Identify the vertices, co-vertices,
and foci. Note that a 2 5
and b 2 5 , so a 5 and
b 5 . The denominator of the
x 2 -term is that
of the y 2 -term, so the major axis
is . The vertices of
the ellipse are at (6a, 0) 5 (6 , 0). The co-vertices
are at (0, 6b) 5 (0, 6 ). Find the foci.
c2 5 a2 2 b2 5 5 , so c 5 Ï }
.
The foci are at (6 Ï }
, 0), or about (6 , 0).
3. Draw the ellipse that passes through each vertex and
co-vertex.
Example 2 Write an equation given a vertex and a co-vertex
Write an equation of the ellipse that has a vertex at
(0, 7), a co-vertex at (24, 0), and center at (0, 0).
Sketch the ellipse as a check for your
final equation. By symmetry, the
y
ellipse must also have a vertex at
(0, ) and a co-vertex at ( , 0).
Because the vertex is on the
2
2
x
and the co-vertex is on the ,
the major axis is with
a 5 , and the minor axis is with b 5 .
An equation is 5 1, or 5 1.
242 Lesson 9.4 Algebra 2 Notetaking Guide Copyright © Holt McDougal. All rights reserved.
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