directrix at
x
=
5
(

1, 5);
1124
CHAPTER 11
Analytic Geometry and Systems of Nonlinear Equations and Inequalities
In Exercises 25–32, find the focus, vertex, directrix, and length of latus rectum and graph the parabola.
25.
26.
27.
28.
29.
30.
31.
32.
In Exercises 33–44, find the vertex and graph the parabola.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
y
2
+
y

x
+
1
=
0
x
2

x
+
y

1
=
0
x
2

6
x

4
y
+
10
=
0
y
2
+
2
y

8
x

23
=
0
x
2

6
x
+
2
y
+
9
=
0
y
2

4
y

2
x
+
4
=
0
y
2
= 
16(
x
+
1)
(
x
+
5)
2
= 
2
y
(
x
+
3)
2
= 
8(
y

2)
(
x

3)
2
= 
8(
y
+
1)
(
y
+
2)
2
= 
4(
x

1)
(
y

2)
2
=
4(
x
+
3)
y
2
= 
16
x
y
2
=
4
x
x
2
= 
8
y
x
2
=
16
y
y
2
=
6
x
y
2
= 
2
x
x
2
= 
12
y
x
2
=
8
y
45.Satellite Dish.A satellite dish measures 8 feet across its opening and 2 feet deep at its center. The receiver should be placed at the focus of the parabolic dish. Where is the focus?
46.Satellite Dish.A satellite dish measures 30 feet across its opening and 5 feet deep at its center. The receiver should be placed at the focus of the parabolic dish. Where is the focus?
48.Optical Lens.A parabolic lens focuses light onto a focalpoint 3 centimeters from the vertex of the lens. How wide isthe lens 0.5 centimeter from the vertex?
©AP/Wide World Photos49.Solar Cooker.The parabolic cooker MSST10 is deliveredas a kit, handily packed in a single carton, with completeassembly instructions and even the necessary tools.
21.
22.
23.
24.
x
y
(–3, –2)
(–3, 6)
Vertex (–1, 2)
x
y
(–2, –3)
(6, –3)
Vertex
(2, –1)
(–2, 1)
(6, 1)
Vertex
(2, –1)
x
y
x
y
(1, –2)
(1, 6)
Vertex (–1, 2)
In Exercises 21–24, write an equation for each parabola.
■
A P P L I C AT I O N S
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 Summer '17
 juan alberto
 Vertex, MAJOR AXIS, Systems of Nonlinear Equations and Inequalities