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) ( x − 4 ) 2 9 − ( y + 2 ) 2 16 = 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) ( x − 4 ) 2 9 − ( y + 2 ) 2 16 = 1
Solution Summary: The author explains that the center of the given hyperbola is (4,-2).
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
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.
Part 2. Find the Standard Equation
3. hyperbola with vertices at (-2, -4), (-2, 6), foci at (-2,-5), (-2,7)
ㅋ
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.