 10.2.1: The set of all points in a plane the sum of whose distances from tw...
 10.2.2: Consider the following equation in standard form: x2 25 + y2 9 = 1....
 10.2.3: Consider the following equation in standard form: x2 9 + y2 25 = 1....
 10.2.4: The graph of (x + 1) 2 25 + (y  4) 2 9 has its center at _________...
 10.2.5: If the center of an ellipse is (3, 2), the major axis is horizonta...
 10.2.6: In Exercises 116, graph each ellipse.x249+ y236 = 1
 10.2.7: In Exercises 116, graph each ellipse.x249+ y281 = 1
 10.2.8: In Exercises 116, graph each ellipse.x264+ y2100 = 1
 10.2.9: In Exercises 116, graph each ellipse.25x2 + 4y2 = 100
 10.2.10: In Exercises 116, graph each ellipse.9x2 + 4y2 = 36
 10.2.11: In Exercises 116, graph each ellipse.4x2 + 16y2 = 64
 10.2.12: In Exercises 116, graph each ellipse.16x2 + 9y2 = 144
 10.2.13: In Exercises 116, graph each ellipse.25x2 + 9y2 = 225
 10.2.14: In Exercises 116, graph each ellipse.4x2 + 25y2 = 100
 10.2.15: In Exercises 116, graph each ellipse.x2 + 2y2 = 8
 10.2.16: In Exercises 116, graph each ellipse.12x2 + 4y2 = 36
 10.2.17: In Exercises 1720, find the standard form of the equation of each e...
 10.2.18: In Exercises 1720, find the standard form of the equation of each e...
 10.2.19: In Exercises 1720, find the standard form of the equation of each e...
 10.2.20: In Exercises 1720, find the standard form of the equation of each e...
 10.2.21: In Exercises 2132, graph each ellipse.(x  2)29+ (y  1)24 = 1
 10.2.22: In Exercises 2132, graph each ellipse.(x  1)216+ (y + 2)29 = 1
 10.2.23: In Exercises 2132, graph each ellipse.(x + 3)2 + 4(y  2)2 = 16
 10.2.24: In Exercises 2132, graph each ellipse.. (x  3)2 + 9(y + 2)2 = 36
 10.2.25: In Exercises 2132, graph each ellipse.(x  4)29+ (y + 2)225 = 1
 10.2.26: In Exercises 2132, graph each ellipse.(x  3)29+ (y + 1)216 = 1
 10.2.27: In Exercises 2132, graph each ellipse.x225+ (y  2)236 = 1
 10.2.28: In Exercises 2132, graph each ellipse.(x  4)24+ y225 = 1
 10.2.29: In Exercises 2132, graph each ellipse.(x + 3)29+ (y  2)2 = 1
 10.2.30: In Exercises 2132, graph each ellipse.(x + 2)216+ (y  3)2 = 1
 10.2.31: In Exercises 2132, graph each ellipse.9(x  1)2 + 4(y + 3)2 = 36
 10.2.32: In Exercises 2132, graph each ellipse.36(x + 4)2 + (y + 3)2 = 36
 10.2.33: In Exercises 3334, find the standard form of the equation of each e...
 10.2.34: In Exercises 3334, find the standard form of the equation of each e...
 10.2.35: In Exercises 3540, find the solution set for each system by graphin...
 10.2.36: In Exercises 3540, find the solution set for each system by graphin...
 10.2.37: In Exercises 3540, find the solution set for each system by graphin...
 10.2.38: In Exercises 3540, find the solution set for each system by graphin...
 10.2.39: In Exercises 3540, find the solution set for each system by graphin...
 10.2.40: In Exercises 3540, find the solution set for each system by graphin...
 10.2.41: In Exercises 4142, graph each semiellipse.y =  216  4x2
 10.2.42: In Exercises 4142, graph each semiellipse.y =  24  4x2
 10.2.43: Will a truck that is 8 feet wide carrying a load that reaches 7 fee...
 10.2.44: A semielliptic archway has a height of 20 feet and a width of 50 fe...
 10.2.45: The elliptical ceiling in Statuary Hall in the U.S. Capitol Buildin...
 10.2.46: If an elliptical whispering room has a height of 30 feet and a widt...
 10.2.47: What is an ellipse?
 10.2.48: Describe how to graph x2 25 + y2 16 = 1.
 10.2.49: Describe one similarity and one difference between the graphs of x2...
 10.2.50: Describe one similarity and one difference between the graphs of x2...
 10.2.51: An elliptipool is an elliptical pool table with only one pocket. A ...
 10.2.52: Use a graphing utility to graph any five of the ellipses that you g...
 10.2.53: Use a graphing utility to graph any three of the ellipses that you ...
 10.2.54: Make Sense? In Exercises 5457, determine whether each statement mak...
 10.2.55: Make Sense? In Exercises 5457, determine whether each statement mak...
 10.2.56: Make Sense? In Exercises 5457, determine whether each statement mak...
 10.2.57: Make Sense? In Exercises 5457, determine whether each statement mak...
 10.2.58: In Exercises 5861, determine whether each statement is true or fals...
 10.2.59: In Exercises 5861, determine whether each statement is true or fals...
 10.2.60: In Exercises 5861, determine whether each statement is true or fals...
 10.2.61: In Exercises 5861, determine whether each statement is true or fals...
 10.2.62: Find the standard form of the equation of an ellipse with vertices ...
 10.2.63: In Exercises 6364, convert each equation to standard form by comple...
 10.2.64: In Exercises 6364, convert each equation to standard form by comple...
 10.2.65: An Earth satellite has an elliptical orbit described by x2 (5000) 2...
 10.2.66: The equation of the red ellipse in the figure shown is x2 25 + y2 9...
 10.2.67: Factor completely: x3 + 2x2  4x  8. (Section 5.5, Example 4)
 10.2.68: Simplify: 3 240x4y7 . (Section 7.3, Example 5)
 10.2.69: Solve: 2 x + 2 + 4 x  2 = x  1 x2  4 . (Section 6.6, Example 5)
 10.2.70: Exercises 7072 will help you prepare for the material covered in th...
 10.2.71: Exercises 7072 will help you prepare for the material covered in th...
 10.2.72: Exercises 7072 will help you prepare for the material covered in th...
Solutions for Chapter 10.2: The Ellipse
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 10.2: The Ellipse
Get Full SolutionsSince 72 problems in chapter 10.2: The Ellipse have been answered, more than 52909 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 10.2: The Ellipse includes 72 full stepbystep solutions. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.