open parenthesis y
−
6 close parenthesis to the 2 power over 4 equals 1
−
open parenthesis x
−
5 close parenthesis to the 2 power over 9
open parenthesis y
−
6 close parenthesis to the 2 power equals 4 open square bracket 1
−
open parenthesis x
−
5 close parenthesis to the 2 power over 9 close square bracket
y equals 6 plus or minus 2 the square root of 1
−
open parenthesis x
−
5 close parenthesis to the 2 power over 9 end radicand
Is it necessary to break up the curve into two halves in order to graph the ellipse? Why or why not?
EXAMPLE 2
Graph
open parenthesis x
−
5 close parenthesis to the 2 power over 9 plus open parenthesis y
−
6 close parenthesis to the 2 power over 4 equals 1.
Solution
The center of the ellipse is (5, 6),
a
= 3, and
b
= 2. Therefore, we begin at (5, 6). We plot points 3 units to the left, 3 units to the right, 2 units up, and 2 units down from (5, 6). The points we plot are the
vertices
of the ellipse.
Student Practice 2
Graph
open parenthesis x
−
2 close parenthesis to the 2 power over 16 plus open parenthesis y plus 3 close parenthesis to the 2 power over 9 equals 1.
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648649
10.3 Exercises: Verbal and Writing Skills, Exercises 1–2
1.Explain how to determine the center of the ellipse 2.Explain how to determine the x- and y-intercepts of the ellipse Graph each ellipse. Label the intercepts. You may need to use a scale other than1 square= 1 unit
.
.
.
3.
4.
5.
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6.
7.
4
x
2
+
y
2
−
36 = 0
8.
9
x
2
+
y
2
−
9 = 0
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9.
x
2
+ 9
y
2
= 81
10.
4
x
2
+ 25
y
2
= 100
11.
x
2
+ 12
y
2
= 36
649650
12.
2
x
2
+ 3
y
2
= 18
13.
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