 10.3.1: The set of all points in a plane the difference of whose distances ...
 10.3.2: The vertices of x2 25  y2 9 = 1 are ______________ and ___________...
 10.3.3: The vertices of y2 25  x2 9 = 1 are ______________ and ___________...
 10.3.4: The two branches of the graph of a hyperbola approach a pair of int...
 10.3.5: The equation 9x2  4y2 = 36 can be written in standard form by ____...
 10.3.6: Identify the graph of each equation as an ellipse, a hyperbola, or ...
 10.3.7: Identify the graph of each equation as an ellipse, a hyperbola, or ...
 10.3.8: Identify the graph of each equation as an ellipse, a hyperbola, or ...
 10.3.9: Identify the graph of each equation as an ellipse, a hyperbola, or ...
 10.3.10: Identify the graph of each equation as an ellipse, a hyperbola, or ...
 10.3.11: In Exercises 518, use vertices and asymptotes to graph each hyperbo...
 10.3.12: In Exercises 518, use vertices and asymptotes to graph each hyperbo...
 10.3.13: In Exercises 518, use vertices and asymptotes to graph each hyperbo...
 10.3.14: In Exercises 518, use vertices and asymptotes to graph each hyperbo...
 10.3.15: In Exercises 518, use vertices and asymptotes to graph each hyperbo...
 10.3.16: In Exercises 518, use vertices and asymptotes to graph each hyperbo...
 10.3.17: In Exercises 518, use vertices and asymptotes to graph each hyperbo...
 10.3.18: In Exercises 518, use vertices and asymptotes to graph each hyperbo...
 10.3.19: In Exercises 1922, find the standard form of the equation of each h...
 10.3.20: In Exercises 1922, find the standard form of the equation of each h...
 10.3.21: In Exercises 1922, find the standard form of the equation of each h...
 10.3.22: In Exercises 1922, find the standard form of the equation of each h...
 10.3.23: n Exercises 2328, graph each relation. Use the relations graph to d...
 10.3.24: n Exercises 2328, graph each relation. Use the relations graph to d...
 10.3.25: n Exercises 2328, graph each relation. Use the relations graph to d...
 10.3.26: n Exercises 2328, graph each relation. Use the relations graph to d...
 10.3.27: n Exercises 2328, graph each relation. Use the relations graph to d...
 10.3.28: n Exercises 2328, graph each relation. Use the relations graph to d...
 10.3.29: In Exercises 2932, find the solution set for each system by graphin...
 10.3.30: In Exercises 2932, find the solution set for each system by graphin...
 10.3.31: In Exercises 2932, find the solution set for each system by graphin...
 10.3.32: In Exercises 2932, find the solution set for each system by graphin...
 10.3.33: An architect designs two houses that are shaped and positioned like...
 10.3.34: Scattering experiments, in which moving particles are deflected by ...
 10.3.35: What is a hyperbola?
 10.3.36: Describe how to graph x2 9  y2 1 = 1.
 10.3.37: Describe one similarity and one difference between the graphs of x2...
 10.3.38: How can you distinguish an ellipse from a hyperbola by looking at t...
 10.3.39: In 1992, a NASA team began a project called Spaceguard Survey, call...
 10.3.40: Use a graphing utility to graph any five of the hyperbolas that you...
 10.3.41: Use a graphing utility to graph x2 4  y2 9 = 0. Is the graph a hyp...
 10.3.42: Graph x2 a2  y2 b2 = 1 and x2 a2  y2 b2 = 1 in the same viewing ...
 10.3.43: Make Sense? In Exercises 4346, determine whether each statement mak...
 10.3.44: Make Sense? In Exercises 4346, determine whether each statement mak...
 10.3.45: Make Sense? In Exercises 4346, determine whether each statement mak...
 10.3.46: Make Sense? In Exercises 4346, determine whether each statement mak...
 10.3.47: In Exercises 4750, determine whether each statement is true or fals...
 10.3.48: In Exercises 4750, determine whether each statement is true or fals...
 10.3.49: In Exercises 4750, determine whether each statement is true or fals...
 10.3.50: In Exercises 4750, determine whether each statement is true or fals...
 10.3.51: The graph of (x  h) 2 a2  (y  k) 2 b2 = 1 is the same as the gra...
 10.3.52: The graph of (x  h) 2 a2  (y  k) 2 b2 = 1 is the same as the gra...
 10.3.53: The graph of (x  h) 2 a2  (y  k) 2 b2 = 1 is the same as the gra...
 10.3.54: The graph of (x  h) 2 a2  (y  k) 2 b2 = 1 is the same as the gra...
 10.3.55: In Exercises 5556, find the standard form of the equation of the hy...
 10.3.56: In Exercises 5556, find the standard form of the equation of the hy...
 10.3.57: Use intercepts and the vertex to graph the quadratic function: y = ...
 10.3.58: Solve: 3x2  11x  4 0. (Section 8.5, Example 1)
 10.3.59: Solve: log4(3x + 1) = 3. (Section 9.5, Example 4)
 10.3.60: Exercises 6062 will help you prepare for the material covered in th...
 10.3.61: Exercises 6062 will help you prepare for the material covered in th...
 10.3.62: Exercises 6062 will help you prepare for the material covered in th...
Solutions for Chapter 10.3: The Hyperbola
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 10.3: The Hyperbola
Get Full SolutionsSince 62 problems in chapter 10.3: The Hyperbola have been answered, more than 45744 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 10.3: The Hyperbola includes 62 full stepbystep solutions. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib IIĀ· Condition numbers measure the sensitivity of the output to change in the input.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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].

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

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

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

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

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

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

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

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).

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Solvable system Ax = b.
The right side b is in the column space of A.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.