
Concept explainers
a.
Find the standard form of the equation.
a.

Answer to Problem 43PPS
(x−3)216+(y+2)24=1
Explanation of Solution
Given information:
An ellipse with centre (3,−2), vertex M(−1,−2), and co-vertex N(3,−4).
Calculation:
As the y− ordinate of vertex and centre is same, the ellipse is horizontal.
Value of a will be the distance between vertex and centre.
a=3−(−1)=4
Value of b will be equal to the distance between co-vertex and centre.
b=(−2)−(−4)=2
Use the equation of an ellipse with horizontal orientation,
(x−h)2a2+(y−k)2b2=1
Substitute (h,k)=(3,−2),a=4,b=2 , the equation of given ellipse will be,
(x−3)242+{y−(−2)}222=1
(x−3)216+(y+2)24=1
b.
Convert in standard form.
b.

Answer to Problem 43PPS
x2+4y2−6x+16y+9=0
Explanation of Solution
Given information:
An ellipse with centre (3,−2), vertex M(−1,−2), and co-vertex N(3,−4).
Ax2+Bxy+Cy2+Dx+Ey+F=0
Calculation:
Convert the equation (1)(x−3)216+(y+2)24=1 to standard form
(x−3)216+(y+2)24=1(x−3)2+4(y+2)2=16x2−6x+9+4y2+16y+16=16x2+4y2−6x+16y+9=0
Hence, standard form of the equation of ellipse is,
x2+4y2−6x+16y+9=0
c.
Graph the ellipse.
c.

Answer to Problem 43PPS
Explanation of Solution
Given information:
An ellipse with centre (3,−2), vertex M(−1,−2), and co-vertex N(3,−4).
Calculation:
The graph is shown below:
d.
Determine the location of N and the angle of rotation.
d.

Answer to Problem 43PPS
Explanation of Solution
Given information:
An ellipse with centre (3,−2), vertex M(−1,−2), and co-vertex N(3,−4).
Calculation:
Distance between new position of point M and centre will be,
(−2)−(−6)=4
By rotating the ellipse in the given manner, the horizontal ellipse will be the “Vertical ellipse”.
Hence, the angle of rotation will be 90°counterclockwise
The new position of point N will have same y−ordiante as of centre and its x−ordinate will be,
(−2)−(−6)=4
Hence, the new position of point N will be (5,−2) .
Chapter 9 Solutions
Glencoe Algebra 2 Student Edition C2014
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Elementary Statistics (13th Edition)
Pre-Algebra Student Edition
Basic Business Statistics, Student Value Edition
A First Course in Probability (10th Edition)
Elementary Statistics: Picturing the World (7th Edition)
- Let R be field and X= R³/s Vector space over R M=(a,b,c)labic, e Rra+b= 3- <3 Show that Ms and why with proof. 1) is convexset and affine set of botost ii) is blanced set and symmetirs set of x iii) is hy per space and hyper plane ofx or hot iii) find f:MR st kerf = M 18/103 and finnd fiM→R/{0} st M= {xEX, f(t) = x, texiαER? jiii) show that Mis Maxsubspace or not and Mis a max. affine set or not.arrow_forwardFind The partial fraction decomposition for each The following 2× B) (x+3) a 3 6 X-3x+2x-6arrow_forward1) Find the partial feraction decomposition for each of 5- X 2 2x+x-1 The following: 3 B) 3 X + 3xarrow_forward
- Kate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). The following table shows the values of the slices in the eyes of each player. What is fair share to nancy? S1 S2 S3 S4 Kate $4.00 $6.00 $6.00 $4.00 Luke $5.30 $5.00 $5.25 $5.45 Mary $4.25 $4.50 $3.50 $3.75 Nancy $6.00 $4.00 $4.00 $6.00arrow_forwardKate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). The following table shows the values of the slices in the eyes of each player. S1 S2 S3 S4 Kate $4.00 $6.00 $6.00 $4.00 Luke $5.30 $5.00 $5.25 $5.45 Mary $4.25 $4.50 $3.50 $3.75 Nancy $6.00 $4.00 $4.00 $6.00 how much is the cak worth to maryarrow_forwardKate, Luke, Mary and Nancy are sharing a cake. The cake had previously been divided into four slices (s1, s2, s3 and s4). The following table shows the values of the slices in the eyes of each player. What is the threshold of fair share for Luke? S1 S2 S3 S4 Kate $4.00 $6.00 $6.00 $4.00 Luke $5.30 $5.00 $5.25 $5.45 Mary $4.25 $4.50 $3.50 $3.75 Nancy $6.00 $4.00 $4.00 $6.00arrow_forward
- 2. A microwave manufacturing firm has determined that their profit function is P(x)=-0.0014x+0.3x²+6x-355 , where is the number of microwaves sold annually. a. Graph the profit function using a calculator. b. Determine a reasonable viewing window for the function. c. Approximate all of the zeros of the function using the CALC menu of your calculator. d. What must be the range of microwaves sold in order for the firm to profit?arrow_forwardA clothing manufacturer's profitability can be modeled by p (x)=-x4 + 40x² - 144, where .x is the number of items sold in thousands and p (x) is the company's profit in thousands of dollars. a. Sketch the function on your calculator and describe the end behavior. b. Determine the zeros of the function. c. Between what two values should the company sell in order to be profitable? d. Explain why only two of the zeros are considered in part c.arrow_forwardCCSS REASONING The number of subscribers using pagers in the United States can be modeled by f(x) = 0.015x4 -0.44x³ +3.46x² - 2.7x+9.68 where x is the number of years after 1990 and f(x) is the number of subscribers in millions. a. Graph the function. b. Describe the end behavior of the graph. c. What does the end behavior suggest about the number of pager subscribers? d. Will this trend continue indefinitely? Explain your reasoning.arrow_forward
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education





