 7.2.1: In Exercises 14, find the vertkes and locate the foci of each hype...
 7.2.2: In Exercises 14, find the vertkes and locate the foci of each hype...
 7.2.3: In Exercises 14, find the vertkes and locate the foci of each hype...
 7.2.4: In Exercises 14, find the vertkes and locate the foci of each hype...
 7.2.5: In Exercises 512, find the standard form of the equation of each h...
 7.2.6: In Exercises 512, find the standard form of the equation of each h...
 7.2.7: In Exercises 512, find the standard form of the equation of each h...
 7.2.8: In Exercises 512, find the standard form of the equation of each h...
 7.2.9: In Exercises 512, find the standard form of the equation of each h...
 7.2.10: In Exercises 512, find the standard form of the equation of each h...
 7.2.11: In Exercises 512, find the standard form of the equation of each h...
 7.2.12: In Exercises 512, find the standard form of the equation of each h...
 7.2.13: In Exercises 1326, use vertices and asymptotes to graph each hyper...
 7.2.14: In Exercises 1326, use vertices and asymptotes to graph each hyper...
 7.2.15: In Exercises 1326, use vertices and asymptotes to graph each hyper...
 7.2.16: In Exercises 1326, use vertices and asymptotes to graph each hyper...
 7.2.17: In Exercises 1326, use vertices and asymptotes to graph each hyper...
 7.2.18: In Exercises 1326, use vertices and asymptotes to graph each hyper...
 7.2.19: In Exercises 1326, use vertices and asymptotes to graph each hyper...
 7.2.20: In Exercises 1326, use vertices and asymptotes to graph each hyper...
 7.2.21: In Exercises 1326, use vertices and asymptotes to graph each hyper...
 7.2.22: In Exercises 1326, use vertices and asymptotes to graph each hyper...
 7.2.23: In Exercises 1326, use vertices and asymptotes to graph each hyper...
 7.2.24: In Exercises 1326, use vertices and asymptotes to graph each hyper...
 7.2.25: In Exercises 1326, use vertices and asymptotes to graph each hyper...
 7.2.26: In Exercises 1326, use vertices and asymptotes to graph each hyper...
 7.2.27: In Exercises 2732, find the standard form of the equation of each ...
 7.2.28: In Exercises 2732, find the standard form of the equation of each ...
 7.2.29: In Exercises 2732, find the standard form of the equation of each ...
 7.2.30: In Exercises 2732, find the standard form of the equation of each ...
 7.2.31: In Exercises 2732, find the standard form of the equation of each ...
 7.2.32: In Exercises 2732, find the standard form of the equation of each ...
 7.2.33: In Exercises 3342, use the center. venices. and asymptotes to grap...
 7.2.34: In Exercises 3342, use the center. venices. and asymptotes to grap...
 7.2.35: In Exercises 3342, use the center. venices. and asymptotes to grap...
 7.2.36: In Exercises 3342, use the center. venices. and asymptotes to grap...
 7.2.37: In Exercises 3342, use the center. venices. and asymptotes to grap...
 7.2.38: In Exercises 3342, use the center. venices. and asymptotes to grap...
 7.2.39: In Exercises 3342, use the center. venices. and asymptotes to grap...
 7.2.40: In Exercises 3342, use the center. venices. and asymptotes to grap...
 7.2.41: In Exercises 3342, use the center. venices. and asymptotes to grap...
 7.2.42: In Exercises 3342, use the center. venices. and asymptotes to grap...
 7.2.43: In Exercises 4350, convert each equation to standard form by compl...
 7.2.44: In Exercises 4350, convert each equation to standard form by compl...
 7.2.45: In Exercises 4350, convert each equation to standard form by compl...
 7.2.46: In Exercises 4350, convert each equation to standard form by compl...
 7.2.47: In Exercises 4350, convert each equation to standard form by compl...
 7.2.48: In Exercises 4350, convert each equation to standard form by compl...
 7.2.49: In Exercises 4350, convert each equation to standard form by compl...
 7.2.50: In Exercises 4350, convert each equation to standard form by compl...
 7.2.51: In Exercises 5156, graph each relation. Use the relation's graph t...
 7.2.52: In Exercises 5156, graph each relation. Use the relation's graph t...
 7.2.53: In Exercises 5156, graph each relation. Use the relation's graph t...
 7.2.54: In Exercises 5156, graph each relation. Use the relation's graph t...
 7.2.55: In Exercises 5156, graph each relation. Use the relation's graph t...
 7.2.56: In Exercises 5156, graph each relation. Use the relation's graph t...
 7.2.57: In Exercises 5760, find the solution set for each system by graphi...
 7.2.58: In Exercises 5760, find the solution set for each system by graphi...
 7.2.59: In Exercises 5760, find the solution set for each system by graphi...
 7.2.60: In Exercises 5760, find the solution set for each system by graphi...
 7.2.61: An explosion is recorded by two microphones that are 1 mile apart. ...
 7.2.62: Radio towers A and 8 , 200 kilomete rs apart. are situated along th...
 7.2.63: An architect designs two houses that are shaped a nd positioned lik...
 7.2.64: Scattering experiments, in which moving pa rticles are deHected by ...
 7.2.65: Moire patterns. such as those shown in Exercises 6566, can appear ...
 7.2.66: Moire patterns. such as those shown in Exercises 6566, can appear ...
 7.2.67: What is a hyperbola?
 7.2.68: Describe how to graph 9  T  1.
 7.2.69: Describe how to locate the foci of the graph of 9  T  I.
 7.2.70: Describe one similarity and one difference between the x' y' y' x' ...
 7.2.71: Describe one similarity and one difference between the x2 y' ~t  3...
 7.2.72: How can you distinguish an ellipse from a hyperbola by looking at t...
 7.2.73: In 1992, a NASA team began a project called Spaceguard Survey, caJi...
 7.2.74: Use a graphing utility to graph any five of the hyperbolas that you...
 7.2.75: Use a graphing utility to graph any three of the hyperbolas that yo...
 7.2.76: Use a graphing utility to graph any one of the hyperbolas that you ...
 7.2.77: Use a graphing utility to graph:  ~  0. Is the graph a \"2 y2 hy...
 7.2.78: Graph     I and '   I in the same viewing al b2 al bl rect...
 7.2.79: Write 4x2  6xy + 2y'  3x + tOy  6  0 as a quadratic equation in...
 7.2.80: Graph i6  9  1 and 1'6  9  I m the same viewing rectangle. Expl...
 7.2.81: In Exercises 8184, determine whether each statement makes sense or...
 7.2.82: In Exercises 8184, determine whether each statement makes sense or...
 7.2.83: In Exercises 8184, determine whether each statement makes sense or...
 7.2.84: In Exercises 8184, determine whether each statement makes sense or...
 7.2.85: In Exercises 8588, determine whether each statement is true or fal...
 7.2.86: In Exercises 8588, determine whether each statement is true or fal...
 7.2.87: In Exercises 8588, determine whether each statement is true or fal...
 7.2.88: In Exercises 8588, determine whether each statement is true or fal...
 7.2.89: What happens to the shape of the graph of a'  b'  1 as  .:o wher...
 7.2.90: Find the standard form of the equation of the hyperbola "1th vertic...
 7.2.91: Find the equation of a hyperbola whose asymptotes are perpendicular.
 7.2.92: Exercises 9294 will help you prepare for the material covered in t...
 7.2.93: Exercises 9294 will help you prepare for the material covered in t...
 7.2.94: Exercises 9294 will help you prepare for the material covered in t...
Solutions for Chapter 7.2: The Hyperbola
Full solutions for College Algebra  6th Edition
ISBN: 9780321782281
Solutions for Chapter 7.2: The Hyperbola
Get Full SolutionsThis textbook survival guide was created for the textbook: College Algebra , edition: 6. Chapter 7.2: The Hyperbola includes 94 full stepbystep solutions. Since 94 problems in chapter 7.2: The Hyperbola have been answered, more than 37095 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9780321782281.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

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

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

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

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

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

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

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.