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 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
2. Suppose that the last three digits of your student number are like. abc . It is not
important whether it is a 4 digit number or a 5 digit number, take the last three
:+(-1) ;
(b+1)3
digits as abc. Consider the conic (-1)ª
following.
Major semiaxis
Minor semiaxis
(-1)ab. Find the
%3D
(a+1)a
i.
ii.
iii.
Vertices
iv.
Foci
Eccentricity
Directrices
Asymptotes (if it is a hyperbola) and the graph (geogebra or nice handmade)
V.
vi.
vii.
Now, consider the Quadratic Surface
(-1)ª.
(a+1)a
+(-1) + (-1)°
(b+1)
=(-1)abe.
(c+1)2
Find the following.
Name of the surface
viii.
ix.
Traces of the surface
Nice Graph (in GeoGebra or handmade)
х.
For example, your professor's ID number is 0000005121. So, he will study the conic
(-1) + (-1) =(-1)*2 which gives (-) +
(-1)',
(1+1)
= (-1)12 which gives (-) +
= 1. Also he will
(2+1)3
4
study the quadratic surface (-1)'
(1+1)2
+ (-1)² -
(2+1)a
+ (-1)';
:(-1)121
(1+1)
which gives. (-) + + (-÷) = 1.
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