1. Exploring Conic Sections
ALGEBRA 2 LESSON 10-1
Graph the equation x2 + y2 = 16. Describe the graph and its lines of symmetry. Then find the domain and range.
x y –
–3 ± ± 2.6
–2 ± ± 3.5
–1 ± ± 3.9 ±4
1 ± ± 3.9
2 ± ± 3.5
3 ± ± 2.6
Make a table of values.
Plot the points and connect them with a smooth curve.
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2. Exploring Conic Sections
ALGEBRA 2 LESSON 10-1
(continued)
The graph is a circle of radius 4. Its center is at the origin. Every line through the center is a line of symmetry.
Recall from Chapter 2 that you can use set notation to describe a domain or a range. In this Example, the domain is {x| – x }. The range is {y| – y }.
< –
10-1

3. Exploring Conic Sections
ALGEBRA 2 LESSON 10-1
Graph the equation 9x y2 = 36. Describe the graph and the lines of symmetry. Then find the domain and range.
x y –
–1 ± 2.6
0 ± 3
1 ± 2.6
Make a table of values.
Plot the points and connect them with smooth curves.
The graph is an ellipse. The center is at the origin. It has two lines of symmetry, the x-axis and the y-axis.
The domain is {x| – x }.
The range is {y| – y }.
< –
10-1

4. Exploring Conic Sections
ALGEBRA 2 LESSON 10-1
Graph the equation x2 – y2 = 4. Describe the graph and its lines of symmetry. Then find the domain and range.
x y
–5 ± 4.6
–4 ± 3.5
–3 ± 2.2 –
– — — —
3 ± 2.2
4 ± 3.5
5 ± 4.6
Make a table of values.
Plot the points and connect them with smooth curves.
10-1

5. Exploring Conic Sections
ALGEBRA 2 LESSON 10-1
(continued)
The graph is a hyperbola that consists of two branches. Its center is at the origin. It has two lines of symmetry, the x-axis and the y-axis.
The domain is {x| x –2 or x }. The range is all real numbers.
> –
<
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6. Exploring Conic Sections
ALGEBRA 2 LESSON 10-1
Identify the center and intercepts of the conic section. Then find the domain and range.
The center of the ellipse is (0, 0).
The x-intercepts are (–5, 0) and (5, 0), and the y-intercepts are (0, –4) and (0, 4).
The domain is {x| – x }. The range is {y| – y }.
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10-1

7. Exploring Conic Sections
ALGEBRA 2 LESSON 10-1
Describe each Moiré pattern as a circle, an ellipse, or a hyperbola. Match it with one of these possible equations,
2x2 – y2 = 16, 25x y2 = 100, or x2 + y2 = 16.
a. b. c.
a. The equation 25x y2 = 100 represents a conic section with two sets of intercepts, (±2, 0) and (0, ±5). Since the intercepts are not equidistant from the center, the equation models an ellipse.
10-1

8. Exploring Conic Sections
ALGEBRA 2 LESSON 10-1
(continued)
a. b. c.
b. The equation x2 + y2 = 16 represents a conic section with two sets of intercepts, (±4, 0) and (0, ±4). Since each intercept is 4 units from the center, the equation models a circle.
c. The equation 2x2 – y2 = 16 represents a conic section with one set of intercepts, (±2 2, 0), so the equation must be a hyperbola.
10-1