For Exercises 23–32, a. Identify the center. b. Identify the vertices. c. Identify the foci. d. Write equations for the asymptotes. e. Graph the hyperbola. (See Example 3) ( y − 5 ) 2 49 − ( x + 3 ) 2 25 = 1
For Exercises 23–32, a. Identify the center. b. Identify the vertices. c. Identify the foci. d. Write equations for the asymptotes. e. Graph the hyperbola. (See Example 3) ( y − 5 ) 2 49 − ( x + 3 ) 2 25 = 1
Solution Summary: The author explains that the center of the given hyperbola is (-3,5).
For Exercises 27–34, an equation of a parabola x = 4py or y = 4px is given.
a. Identify the vertex, value of p, focus, and focal diameter of the parabola.
b. Identify the endpoints of the latus rectum.
c. Graph the parabola.
d. Write equations for the directrix and axis of symmetry. (See Examples 2-3)
27. x
-4y
28. x
-20y
29. 10y
= 80x
30. 3y = 12x
31. 4x
40y
32. 2x
14y
33. y =
34. y = -2x
= -X
%3D
For Exercises 67–70, identify the equation as representing an ellipse or a hyperbola, and match the equation with the graph.
(x – 5)²
67.
(y + 2)²
= 1
(x – 5)?
68.
(y + 2)?
= 1
49
36
36
49
(x - 5)?
69.
(y + 2)²
= 1
(y + 2)²
= 1
(x - 5)?
49
36
70.
49
36
А.
В.
С.
D.
15
12
41
6
-6-4-2
4 6 8 10 12 14
4 6 8 10 12 14
-6 -4
2.
4 6 8 10l 12 14
-6
1k 15 18 21
-6
2. Graph the parabola given by the equation, put it into standard form, and identify the vertex,
focus and directrix.
0 = x² - 4x - 8y - 4
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