 11.6.1: Exer. 112: Find the eccentricity, and classify the conic. Sketch th...
 11.6.2: Exer. 112: Find the eccentricity, and classify the conic. Sketch th...
 11.6.3: Exer. 112: Find the eccentricity, and classify the conic. Sketch th...
 11.6.4: Exer. 112: Find the eccentricity, and classify the conic. Sketch th...
 11.6.5: Exer. 112: Find the eccentricity, and classify the conic. Sketch th...
 11.6.6: Exer. 112: Find the eccentricity, and classify the conic. Sketch th...
 11.6.7: Exer. 112: Find the eccentricity, and classify the conic. Sketch th...
 11.6.8: Exer. 112: Find the eccentricity, and classify the conic. Sketch th...
 11.6.9: Exer. 112: Find the eccentricity, and classify the conic. Sketch th...
 11.6.10: Exer. 112: Find the eccentricity, and classify the conic. Sketch th...
 11.6.11: Exer. 112: Find the eccentricity, and classify the conic. Sketch th...
 11.6.12: Exer. 112: Find the eccentricity, and classify the conic. Sketch th...
 11.6.13: Exer. 1324: Find equations in x and y for the polar equations in Ex...
 11.6.14: Exer. 1324: Find equations in x and y for the polar equations in Ex...
 11.6.15: Exer. 1324: Find equations in x and y for the polar equations in Ex...
 11.6.16: Exer. 1324: Find equations in x and y for the polar equations in Ex...
 11.6.17: Exer. 1324: Find equations in x and y for the polar equations in Ex...
 11.6.18: Exer. 1324: Find equations in x and y for the polar equations in Ex...
 11.6.19: Exer. 1324: Find equations in x and y for the polar equations in Ex...
 11.6.20: Exer. 1324: Find equations in x and y for the polar equations in Ex...
 11.6.21: Exer. 1324: Find equations in x and y for the polar equations in Ex...
 11.6.22: Exer. 1324: Find equations in x and y for the polar equations in Ex...
 11.6.23: Exer. 1324: Find equations in x and y for the polar equations in Ex...
 11.6.24: Exer. 1324: Find equations in x and y for the polar equations in Ex...
 11.6.25: Exer. 2532: Find a polar equation of the conic with focus at the po...
 11.6.26: Exer. 2532: Find a polar equation of the conic with focus at the po...
 11.6.27: Exer. 2532: Find a polar equation of the conic with focus at the po...
 11.6.28: Exer. 2532: Find a polar equation of the conic with focus at the po...
 11.6.29: Exer. 2532: Find a polar equation of the conic with focus at the po...
 11.6.30: Exer. 2532: Find a polar equation of the conic with focus at the po...
 11.6.31: Exer. 2532: Find a polar equation of the conic with focus at the po...
 11.6.32: Exer. 2532: Find a polar equation of the conic with focus at the po...
 11.6.33: Exer. 3334: Find a polar equation of the parabola with focus at the...
 11.6.34: Exer. 3334: Find a polar equation of the parabola with focus at the...
 11.6.35: Exer. 3536: An ellipse has a focus at the pole with the given cente...
 11.6.36: Exer. 3536: An ellipse has a focus at the pole with the given cente...
 11.6.37: Keplers first law asserts that planets travel in elliptical orbits ...
 11.6.38: Refer to Exercise 37. The planet Pluto travels in an elliptical orb...
 11.6.39: The closest Earth gets to the sun is about 91,405,950 miles, and th...
Solutions for Chapter 11.6: Polar Equations of Conics
Full solutions for Algebra and Trigonometry with Analytic Geometry  12th Edition
ISBN: 9780495559719
Solutions for Chapter 11.6: Polar Equations of Conics
Get Full SolutionsThis textbook survival guide was created for the textbook: Algebra and Trigonometry with Analytic Geometry, edition: 12. This expansive textbook survival guide covers the following chapters and their solutions. Algebra and Trigonometry with Analytic Geometry was written by and is associated to the ISBN: 9780495559719. Chapter 11.6: Polar Equations of Conics includes 39 full stepbystep solutions. Since 39 problems in chapter 11.6: Polar Equations of Conics have been answered, more than 37391 students have viewed full stepbystep solutions from this chapter.

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.)

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

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.

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.

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

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.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

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.

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).

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Outer product uv T
= column times row = rank one matrix.

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

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

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

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

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

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.