 8.2.1: Define a hyperbola in terms of its foci.
 8.2.2: What can we conclude about a hyperbola if its asymptotes intersect ...
 8.2.3: What must be true of the foci of a hyperbola?
 8.2.4: If the transverse axis of a hyperbola is vertical, what do we know ...
 8.2.5: Where must the center of hyperbola be relative to its foci?
 8.2.6: For the following exercises, determine whether the following equati...
 8.2.7: For the following exercises, determine whether the following equati...
 8.2.8: For the following exercises, determine whether the following equati...
 8.2.9: For the following exercises, determine whether the following equati...
 8.2.10: For the following exercises, determine whether the following equati...
 8.2.11: For the following exercises, write the equation for the hyperbola i...
 8.2.12: For the following exercises, write the equation for the hyperbola i...
 8.2.13: For the following exercises, write the equation for the hyperbola i...
 8.2.14: For the following exercises, write the equation for the hyperbola i...
 8.2.15: For the following exercises, write the equation for the hyperbola i...
 8.2.16: For the following exercises, write the equation for the hyperbola i...
 8.2.17: For the following exercises, write the equation for the hyperbola i...
 8.2.18: For the following exercises, write the equation for the hyperbola i...
 8.2.19: For the following exercises, write the equation for the hyperbola i...
 8.2.20: For the following exercises, write the equation for the hyperbola i...
 8.2.21: For the following exercises, write the equation for the hyperbola i...
 8.2.22: For the following exercises, write the equation for the hyperbola i...
 8.2.23: For the following exercises, write the equation for the hyperbola i...
 8.2.24: For the following exercises, write the equation for the hyperbola i...
 8.2.25: For the following exercises, write the equation for the hyperbola i...
 8.2.26: For the following exercises, find the equations of the asymptotes f...
 8.2.27: For the following exercises, find the equations of the asymptotes f...
 8.2.28: For the following exercises, find the equations of the asymptotes f...
 8.2.29: For the following exercises, find the equations of the asymptotes f...
 8.2.30: For the following exercises, find the equations of the asymptotes f...
 8.2.31: For the following exercises, sketch a graph of the hyperbola, label...
 8.2.32: For the following exercises, sketch a graph of the hyperbola, label...
 8.2.33: For the following exercises, sketch a graph of the hyperbola, label...
 8.2.34: For the following exercises, sketch a graph of the hyperbola, label...
 8.2.35: For the following exercises, sketch a graph of the hyperbola, label...
 8.2.36: For the following exercises, sketch a graph of the hyperbola, label...
 8.2.37: For the following exercises, sketch a graph of the hyperbola, label...
 8.2.38: For the following exercises, sketch a graph of the hyperbola, label...
 8.2.39: For the following exercises, sketch a graph of the hyperbola, label...
 8.2.40: For the following exercises, sketch a graph of the hyperbola, label...
 8.2.41: For the following exercises, sketch a graph of the hyperbola, label...
 8.2.42: For the following exercises, sketch a graph of the hyperbola, label...
 8.2.43: For the following exercises, sketch a graph of the hyperbola, label...
 8.2.44: For the following exercises, sketch a graph of the hyperbola, label...
 8.2.45: For the following exercises, given information about the graph of t...
 8.2.46: For the following exercises, given information about the graph of t...
 8.2.47: For the following exercises, given information about the graph of t...
 8.2.48: For the following exercises, given information about the graph of t...
 8.2.49: For the following exercises, given information about the graph of t...
 8.2.50: For the following exercises, given information about the graph of t...
 8.2.51: For the following exercises, given the graph of the hyperbola, find...
 8.2.52: For the following exercises, given the graph of the hyperbola, find...
 8.2.53: For the following exercises, given the graph of the hyperbola, find...
 8.2.54: For the following exercises, given the graph of the hyperbola, find...
 8.2.55: For the following exercises, given the graph of the hyperbola, find...
 8.2.56: For the following exercises, express the equation for the hyperbola...
 8.2.57: For the following exercises, express the equation for the hyperbola...
 8.2.58: For the following exercises, express the equation for the hyperbola...
 8.2.59: For the following exercises, express the equation for the hyperbola...
 8.2.60: For the following exercises, express the equation for the hyperbola...
 8.2.61: For the following exercises, a hedge is to be constructed in the sh...
 8.2.62: For the following exercises, a hedge is to be constructed in the sh...
 8.2.63: For the following exercises, a hedge is to be constructed in the sh...
 8.2.64: For the following exercises, a hedge is to be constructed in the sh...
 8.2.65: For the following exercises, a hedge is to be constructed in the sh...
 8.2.66: For the following exercises, assume an object enters our solar syst...
 8.2.67: For the following exercises, assume an object enters our solar syst...
 8.2.68: For the following exercises, assume an object enters our solar syst...
 8.2.69: For the following exercises, assume an object enters our solar syst...
 8.2.70: For the following exercises, assume an object enters our solar syst...
Solutions for Chapter 8.2: THE HYPERBOLA
Full solutions for College Algebra  1st Edition
ISBN: 9781938168383
Solutions for Chapter 8.2: THE HYPERBOLA
Get Full SolutionsChapter 8.2: THE HYPERBOLA includes 70 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: College Algebra, edition: 1. Since 70 problems in chapter 8.2: THE HYPERBOLA have been answered, more than 34945 students have viewed full stepbystep solutions from this chapter. College Algebra was written by and is associated to the ISBN: 9781938168383.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

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.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

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

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

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

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

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.

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

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.