 8.5.1: Explain how eccentricity determines which conic section is given.
 8.5.2: If a conic section is written as a polar equation, what must be tru...
 8.5.3: If a conic section is written as a polar equation, and the denomina...
 8.5.4: If the directrix of a conic section is perpendicular to the polar a...
 8.5.5: What do we know about the focus/foci of a conic section if it is wr...
 8.5.6: For the following exercises, identify the conic with a focus at the...
 8.5.7: For the following exercises, identify the conic with a focus at the...
 8.5.8: For the following exercises, identify the conic with a focus at the...
 8.5.9: For the following exercises, identify the conic with a focus at the...
 8.5.10: For the following exercises, identify the conic with a focus at the...
 8.5.11: For the following exercises, identify the conic with a focus at the...
 8.5.12: For the following exercises, identify the conic with a focus at the...
 8.5.13: For the following exercises, identify the conic with a focus at the...
 8.5.14: For the following exercises, identify the conic with a focus at the...
 8.5.15: For the following exercises, identify the conic with a focus at the...
 8.5.16: For the following exercises, identify the conic with a focus at the...
 8.5.17: For the following exercises, identify the conic with a focus at the...
 8.5.18: For the following exercises, convert the polar equation of a conic ...
 8.5.19: For the following exercises, convert the polar equation of a conic ...
 8.5.20: For the following exercises, convert the polar equation of a conic ...
 8.5.21: For the following exercises, convert the polar equation of a conic ...
 8.5.22: For the following exercises, convert the polar equation of a conic ...
 8.5.23: For the following exercises, convert the polar equation of a conic ...
 8.5.24: For the following exercises, convert the polar equation of a conic ...
 8.5.25: For the following exercises, convert the polar equation of a conic ...
 8.5.26: For the following exercises, convert the polar equation of a conic ...
 8.5.27: For the following exercises, convert the polar equation of a conic ...
 8.5.28: For the following exercises, convert the polar equation of a conic ...
 8.5.29: For the following exercises, convert the polar equation of a conic ...
 8.5.30: For the following exercises, convert the polar equation of a conic ...
 8.5.31: For the following exercises, graph the given conic section. If it i...
 8.5.32: For the following exercises, graph the given conic section. If it i...
 8.5.33: For the following exercises, graph the given conic section. If it i...
 8.5.34: For the following exercises, graph the given conic section. If it i...
 8.5.35: For the following exercises, graph the given conic section. If it i...
 8.5.36: For the following exercises, graph the given conic section. If it i...
 8.5.37: For the following exercises, graph the given conic section. If it i...
 8.5.38: For the following exercises, graph the given conic section. If it i...
 8.5.39: For the following exercises, graph the given conic section. If it i...
 8.5.40: For the following exercises, graph the given conic section. If it i...
 8.5.41: For the following exercises, graph the given conic section. If it i...
 8.5.42: For the following exercises, graph the given conic section. If it i...
 8.5.43: For the following exercises, find the polar equation of the conic w...
 8.5.44: For the following exercises, find the polar equation of the conic w...
 8.5.45: For the following exercises, find the polar equation of the conic w...
 8.5.46: For the following exercises, find the polar equation of the conic w...
 8.5.47: For the following exercises, find the polar equation of the conic w...
 8.5.48: For the following exercises, find the polar equation of the conic w...
 8.5.49: For the following exercises, find the polar equation of the conic w...
 8.5.50: For the following exercises, find the polar equation of the conic w...
 8.5.51: For the following exercises, find the polar equation of the conic w...
 8.5.52: For the following exercises, find the polar equation of the conic w...
 8.5.53: For the following exercises, find the polar equation of the conic w...
 8.5.54: For the following exercises, find the polar equation of the conic w...
 8.5.55: For the following exercises, find the polar equation of the conic w...
 8.5.56: Recall from Rotation of Axes that equations of conics with an xy te...
 8.5.57: Recall from Rotation of Axes that equations of conics with an xy te...
 8.5.58: Recall from Rotation of Axes that equations of conics with an xy te...
 8.5.59: Recall from Rotation of Axes that equations of conics with an xy te...
 8.5.60: Recall from Rotation of Axes that equations of conics with an xy te...
Solutions for Chapter 8.5: CONIC SECTIONS IN POLAR COORDINATES
Full solutions for College Algebra  1st Edition
ISBN: 9781938168383
Solutions for Chapter 8.5: CONIC SECTIONS IN POLAR COORDINATES
Get Full SolutionsChapter 8.5: CONIC SECTIONS IN POLAR COORDINATES includes 60 full stepbystep solutions. College Algebra was written by and is associated to the ISBN: 9781938168383. This textbook survival guide was created for the textbook: College Algebra, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Since 60 problems in chapter 8.5: CONIC SECTIONS IN POLAR COORDINATES have been answered, more than 31991 students have viewed full stepbystep solutions from this chapter.

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 II· Condition numbers measure the sensitivity of the output to change in the input.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

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

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

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.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

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

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

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).

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

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).

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

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

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

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).