Precalculus Practice Test 9.19.3 - South Minneapolis High School Page 4
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9Precalculus Practice Test 9.1-9.3
7. Find the standard form or the equation of the ellipse with vertices (9, 0) and
1
e .
eccentricity
3
Since the vertices are located at (+9, 0), we can conclude that the center of the ellipse is the
midpoint of the vertices, the origin. We can also conclude that the ellipse is horizontal. The
x h
2
y k
2
1
standard equation for such an ellipse is
.
2
2
a
b
a is the distance from the vertices to the center, so we can conclude that a is 9.
c
e
We know that the eccentricity is given by the equation
, so we can use this to find c.
a
c
c
1
e
. From this, we can conclude that c is equal to 3.
a
9
3
a
b
2
2
2
We also know that
c
. We can plug in the values we know to solve for b.
a
b
2
2
2
c
9
b
2
2
2
3
9 81 b
2
b
72
2
72
2
b
b 72 6 2
Putting all of this together, we find that the equation for the ellipse is
x 0
y 0
2
2
1
2
2
9
72
2
2
x
y
1
81
72
Page 4
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