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Example 4 Write an equation of a translated ellipse
Write an equation of the ellipse with foci at (22, 3) and
(4, 3) and co-vertices at (1, 4) and (1, 2).
1. Determine the form of the
equation. First sketch the
ellipse. The foci lie on the
major axis, so the axis is
y
. The equation
1
has the form:
1
x
(x 2 h)2 (y 2 k)2
} 1 } 5 1
a2 b2 2. Identify h and k by finding the center, which is halfway
between the foci (or the co-vertices).
(h, k) 5 1 , 2 5 ( , )
3. Find b, the distance between a co-vertex and the
center, and c, the distance between a focus and
the center:
b 5 ⏐ ⏐ 5 , c 5 ⏐ ⏐ 5 3.
4. Find a. For an ellipse,
a2 5 b2 1 c2 5 1 5 , so a 5 Ï }
.
The standard form of the equation is
Checkpoint Complete the following exercise.
Copyright © Holt McDougal. All rights reserved. Lesson 9.6 Algebra 2 Notetaking Guide 251
.
4. Write an equation of the ellipse with foci at (23, 0)
and (23, 26) and co-vertices at (21, 23) and
(25, 23).