 10.4.1: The distance d from P1 = 13, 42 to P2 = 1 2, 12 is d = . (p. 5)
 10.4.2: To complete the square of x2 + 5x, add . (pp. A28A29)
 10.4.3: To complete the square of x2 + 5x, add . (pp. A28A29)
 10.4.4: True or False The equation y2 = 9 + x2 is symmetric with
 10.4.5: To graph y = 1x  523  4, shift the graph of y = x3 to the (left/r...
 10.4.6: Find the vertical asymptotes, if any, and the horizontal or oblique...
 10.4.7: A(n) is the collection of points in the plane the difference of who...
 10.4.8: For a hyperbola, the foci lie on a line called the
 10.4.9: The equation of the hyperbola is of the form (a) 1x  h22 a2  1y ...
 10.4.10: If the center of the hyperbola is (2, 1) and a = 3, then the coordi...
 10.4.11: If the center of the hyperbola is (2, 1) and c = 5, then the coordi...
 10.4.12: In a hyperbola, if a = 3 and c = 5, then b .
 10.4.13: For the hyperbola x2 4  y2 9 = 1, the value of a is , the value of...
 10.4.14: For the hyperbola y2 16  x2 81 = 1, the asymptotes are and .
 10.4.15: In 1518, the graph of a hyperbola is given. Match each graph to its...
 10.4.16: In 1518, the graph of a hyperbola is given. Match each graph to its...
 10.4.17: In 1518, the graph of a hyperbola is given. Match each graph to its...
 10.4.18: In 1518, the graph of a hyperbola is given. Match each graph to its...
 10.4.19: In 1928, find an equation for the hyperbola described. Graph the eq...
 10.4.20: In 1928, find an equation for the hyperbola described. Graph the eq...
 10.4.21: In 1928, find an equation for the hyperbola described. Graph the eq...
 10.4.22: In 1928, find an equation for the hyperbola described. Graph the eq...
 10.4.23: In 1928, find an equation for the hyperbola described. Graph the eq...
 10.4.24: In 1928, find an equation for the hyperbola described. Graph the eq...
 10.4.25: In 1928, find an equation for the hyperbola described. Graph the eq...
 10.4.26: In 1928, find an equation for the hyperbola described. Graph the eq...
 10.4.27: In 1928, find an equation for the hyperbola described. Graph the eq...
 10.4.28: In 1928, find an equation for the hyperbola described. Graph the eq...
 10.4.29: In 2936, find the center, transverse axis, vertices, foci, and asym...
 10.4.30: In 2936, find the center, transverse axis, vertices, foci, and asym...
 10.4.31: In 2936, find the center, transverse axis, vertices, foci, and asym...
 10.4.32: In 2936, find the center, transverse axis, vertices, foci, and asym...
 10.4.33: In 2936, find the center, transverse axis, vertices, foci, and asym...
 10.4.34: In 2936, find the center, transverse axis, vertices, foci, and asym...
 10.4.35: In 2936, find the center, transverse axis, vertices, foci, and asym...
 10.4.36: In 2936, find the center, transverse axis, vertices, foci, and asym...
 10.4.37: In 3740, write an equation for each hyperbola.
 10.4.38: In 3740, write an equation for each hyperbola.
 10.4.39: In 3740, write an equation for each hyperbola.
 10.4.40: In 3740, write an equation for each hyperbola.
 10.4.41: In 41 48, find an equation for the hyperbola described. Graph the e...
 10.4.42: In 41 48, find an equation for the hyperbola described. Graph the e...
 10.4.43: In 41 48, find an equation for the hyperbola described. Graph the e...
 10.4.44: In 41 48, find an equation for the hyperbola described. Graph the e...
 10.4.45: In 41 48, find an equation for the hyperbola described. Graph the e...
 10.4.46: In 41 48, find an equation for the hyperbola described. Graph the e...
 10.4.47: In 41 48, find an equation for the hyperbola described. Graph the e...
 10.4.48: In 41 48, find an equation for the hyperbola described. Graph the e...
 10.4.49: In 49 62, find the center, transverse axis, vertices, foci, and asy...
 10.4.50: In 49 62, find the center, transverse axis, vertices, foci, and asy...
 10.4.51: In 49 62, find the center, transverse axis, vertices, foci, and asy...
 10.4.52: In 49 62, find the center, transverse axis, vertices, foci, and asy...
 10.4.53: In 49 62, find the center, transverse axis, vertices, foci, and asy...
 10.4.54: In 49 62, find the center, transverse axis, vertices, foci, and asy...
 10.4.55: In 49 62, find the center, transverse axis, vertices, foci, and asy...
 10.4.56: In 49 62, find the center, transverse axis, vertices, foci, and asy...
 10.4.57: In 49 62, find the center, transverse axis, vertices, foci, and asy...
 10.4.58: In 49 62, find the center, transverse axis, vertices, foci, and asy...
 10.4.59: In 49 62, find the center, transverse axis, vertices, foci, and asy...
 10.4.60: In 49 62, find the center, transverse axis, vertices, foci, and asy...
 10.4.61: In 49 62, find the center, transverse axis, vertices, foci, and asy...
 10.4.62: In 49 62, find the center, transverse axis, vertices, foci, and asy...
 10.4.63: In 63 66, graph each function by hand. Be sure to label any interce...
 10.4.64: In 63 66, graph each function by hand. Be sure to label any interce...
 10.4.65: In 63 66, graph each function by hand. Be sure to label any interce...
 10.4.66: In 6774, analyze each conic.
 10.4.67: In 6774, analyze each conic.
 10.4.68: In 6774, analyze each conic.
 10.4.69: In 6774, analyze each conic.
 10.4.70: In 6774, analyze each conic.
 10.4.71: In 6774, analyze each conic.
 10.4.72: In 6774, analyze each conic.
 10.4.73: In 6774, analyze each conic.
 10.4.74: In 6774, analyze each conic.
 10.4.75: Suppose that two people standing 2 miles apart both see the burst f...
 10.4.76: Suppose that two people standing 2 miles apart both see the burst f...
 10.4.77: Some nuclear power plants utilize natural draft cooling towers in t...
 10.4.78: Some nuclear power plants utilize natural draft cooling towers in t...
 10.4.79: In May 1911, Ernest Rutherford published a paper in Philosophical M...
 10.4.80: Hyperbolas have interesting reflective properties that make them us...
 10.4.81: The eccentricity e of a hyperbola is defined as the number c a , wh...
 10.4.82: A hyperbola for which a = b is called an equilateral hyperbola. Fin...
 10.4.83: Two hyperbolas that have the same set of asymptotes are called conj...
 10.4.84: Prove that the hyperbola y2 a2  x2 b2 = 1 has the two oblique asym...
 10.4.85: Show that the graph of an equation of the form Ax2 + Cy2 + F = 0 A ...
 10.4.86: Show that the graph of an equation of the form Ax2 + Cy2 + Dx + Ey ...
Solutions for Chapter 10.4: The Hyperbola
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 10.4: The Hyperbola
Get Full SolutionsChapter 10.4: The Hyperbola includes 86 full stepbystep solutions. Since 86 problems in chapter 10.4: The Hyperbola have been answered, more than 56134 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351. This expansive textbook survival guide covers the following chapters and their solutions.

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

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

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

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

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

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

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

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.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

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.

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

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