 7.1: In Exercises 18, graph each ellipse and locate the foci. xl y2t. 3...
 7.2: In Exercises 18, graph each ellipse and locate the foci. y2 x 225+...
 7.3: In Exercises 18, graph each ellipse and locate the foci. 4x2 + y2 ...
 7.4: In Exercises 18, graph each ellipse and locate the foci. 4x1 ~ 9y2...
 7.5: In Exercises 18, graph each ellipse and locate the foci. (x 1)2 (...
 7.6: In Exercises 18, graph each ellipse and locate the foci. (x+ 1)' (...
 7.7: In Exercises 18, graph each ellipse and locate the foci. 4x2 + 9y'...
 7.8: In Exercises 18, graph each ellipse and locate the foci. 9x1 + 4y2...
 7.9: In Exercises 911, find tire standard form of the equation of each ...
 7.10: In Exercises 911, find tire standard form of the equation of each ...
 7.11: In Exercises 911, find tire standard form of the equation of each ...
 7.12: A semielliptical arch supports a bridge that spans a river 20 yards...
 7.13: A semielliptic archway has a he ight of 15 feet at the ce nter and ...
 7.14: An elliptical pool table has a ball placed at each focus. If one ba...
 7.15: In Exercises 1522, graph each ilyperbola. Locate the foci and find...
 7.16: In Exercises 1522, graph each ilyperbola. Locate the foci and find...
 7.17: In Exercises 1522, graph each ilyperbola. Locate the foci and find...
 7.18: In Exercises 1522, graph each ilyperbola. Locate the foci and find...
 7.19: In Exercises 1522, graph each ilyperbola. Locate the foci and find...
 7.20: In Exercises 1522, graph each ilyperbola. Locate the foci and find...
 7.21: In Exercises 1522, graph each ilyperbola. Locate the foci and find...
 7.22: In Exercises 1522, graph each ilyperbola. Locate the foci and find...
 7.23: In Exercises 2324, find the nandard form of the equation of each h...
 7.24: In Exercises 2324, find the nandard form of the equation of each h...
 7.25: Explain why it is not possible for a hyperbola to have foci at (0,...
 7.26: Radio tower M2 is located 200 p A miles due wesl of radio tO\ver M ...
 7.27: In Exercises 2733, find the vertex) focus, and directrix of each p...
 7.28: In Exercises 2733, find the vertex) focus, and directrix of each p...
 7.29: In Exercises 2733, find the vertex) focus, and directrix of each p...
 7.30: In Exercises 2733, find the vertex) focus, and directrix of each p...
 7.31: In Exercises 2733, find the vertex) focus, and directrix of each p...
 7.32: In Exercises 2733, find the vertex) focus, and directrix of each p...
 7.33: In Exercises 2733, find the vertex) focus, and directrix of each p...
 7.34: In Exercises 3435, find the standard form of the eqtwtion of each ...
 7.35: In Exercises 3435, find the standard form of the eqtwtion of each ...
 7.36: An engineer is designing headlight units for automobiles. The unit ...
 7.37: The George Washington Bridge spans the Hudson River from New York t...
 7.38: The giant satellite dish in the figure s.hown is in the shape of a ...
Solutions for Chapter 7: Conic Sections
Full solutions for College Algebra  6th Edition
ISBN: 9780321782281
Solutions for Chapter 7: Conic Sections
Get Full SolutionsThis textbook survival guide was created for the textbook: College Algebra , edition: 6. Since 38 problems in chapter 7: Conic Sections have been answered, more than 35188 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 7: Conic Sections includes 38 full stepbystep solutions. College Algebra was written by and is associated to the ISBN: 9780321782281.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Column space C (A) =
space of all combinations of the columns of A.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

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).

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

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

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

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).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

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.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.