 4.3.1: Fill in the blanks. A ________ is the intersection of a plane and a...
 4.3.2: Fill in the blanks. The equation is the standard form of the equati...
 4.3.3: Fill in the blanks. A ________ is the set of all points in a plane ...
 4.3.4: Fill in the blanks. The ________ of a parabola is the midpoint betw...
 4.3.5: Fill in the blanks. The line that passes through the focus and the ...
 4.3.6: Fill in the blanks. An ________ is the set of all points in a plane...
 4.3.7: Fill in the blanks. The chord joining the vertices of an ellipse is...
 4.3.8: Fill in the blanks. The chord perpendicular to the major axis at th...
 4.3.9: Fill in the blanks. A ________ is the set of all points in a plane,...
 4.3.10: Fill in the blanks. The line segment connecting the vertices of a h...
 4.3.11: In Exercises 1120, match the equation with its graph. If the graph ...
 4.3.12: In Exercises 1120, match the equation with its graph. If the graph ...
 4.3.13: In Exercises 1120, match the equation with its graph. If the graph ...
 4.3.14: In Exercises 1120, match the equation with its graph. If the graph ...
 4.3.15: In Exercises 1120, match the equation with its graph. If the graph ...
 4.3.16: In Exercises 1120, match the equation with its graph. If the graph ...
 4.3.17: In Exercises 1120, match the equation with its graph. If the graph ...
 4.3.18: In Exercises 1120, match the equation with its graph. If the graph ...
 4.3.19: In Exercises 1120, match the equation with its graph. If the graph ...
 4.3.20: In Exercises 1120, match the equation with its graph. If the graph ...
 4.3.21: In Exercises 2126, find the vertex and focus of the parabola and sk...
 4.3.22: In Exercises 2126, find the vertex and focus of the parabola and sk...
 4.3.23: In Exercises 2126, find the vertex and focus of the parabola and sk...
 4.3.24: In Exercises 2126, find the vertex and focus of the parabola and sk...
 4.3.25: In Exercises 2126, find the vertex and focus of the parabola and sk...
 4.3.26: In Exercises 2126, find the vertex and focus of the parabola and sk...
 4.3.27: In Exercises 2738, find the standard form of the equation of the pa...
 4.3.28: In Exercises 2738, find the standard form of the equation of the pa...
 4.3.29: In Exercises 2738, find the standard form of the equation of the pa...
 4.3.30: In Exercises 2738, find the standard form of the equation of the pa...
 4.3.31: In Exercises 2738, find the standard form of the equation of the pa...
 4.3.32: In Exercises 2738, find the standard form of the equation of the pa...
 4.3.33: In Exercises 2738, find the standard form of the equation of the pa...
 4.3.34: In Exercises 2738, find the standard form of the equation of the pa...
 4.3.35: In Exercises 2738, find the standard form of the equation of the pa...
 4.3.36: In Exercises 2738, find the standard form of the equation of the pa...
 4.3.37: In Exercises 2738, find the standard form of the equation of the pa...
 4.3.38: In Exercises 2738, find the standard form of the equation of the pa...
 4.3.39: In Exercises 39 42, find the standard form of the equation of the p...
 4.3.40: In Exercises 39 42, find the standard form of the equation of the p...
 4.3.41: In Exercises 39 42, find the standard form of the equation of the p...
 4.3.42: In Exercises 39 42, find the standard form of the equation of the p...
 4.3.43: FLASHLIGHT The light bulb in a flashlight is at the focus of the pa...
 4.3.44: SATELLITE ANTENNA Write an equation for a cross section of the para...
 4.3.45: SUSPENSION BRIDGE Each cable of the Golden Gate Bridge is suspended...
 4.3.46: BEAM DEFLECTION A simply supported beam (see figure) is 64 feet lon...
 4.3.47: In Exercises 4756, find the center and vertices of the ellipse and ...
 4.3.48: In Exercises 4756, find the center and vertices of the ellipse and ...
 4.3.49: In Exercises 4756, find the center and vertices of the ellipse and ...
 4.3.50: In Exercises 4756, find the center and vertices of the ellipse and ...
 4.3.51: In Exercises 4756, find the center and vertices of the ellipse and ...
 4.3.52: In Exercises 4756, find the center and vertices of the ellipse and ...
 4.3.53: In Exercises 4756, find the center and vertices of the ellipse and ...
 4.3.54: In Exercises 4756, find the center and vertices of the ellipse and ...
 4.3.55: In Exercises 4756, find the center and vertices of the ellipse and ...
 4.3.56: In Exercises 4756, find the center and vertices of the ellipse and ...
 4.3.57: In Exercises 5766, find the standard form of the equation of the el...
 4.3.58: In Exercises 5766, find the standard form of the equation of the el...
 4.3.59: In Exercises 5766, find the standard form of the equation of the el...
 4.3.60: In Exercises 5766, find the standard form of the equation of the el...
 4.3.61: In Exercises 5766, find the standard form of the equation of the el...
 4.3.62: In Exercises 5766, find the standard form of the equation of the el...
 4.3.63: In Exercises 5766, find the standard form of the equation of the el...
 4.3.64: In Exercises 5766, find the standard form of the equation of the el...
 4.3.65: In Exercises 5766, find the standard form of the equation of the el...
 4.3.66: In Exercises 5766, find the standard form of the equation of the el...
 4.3.67: ARCHITECTURE A fireplace arch is to be constructed in the shape of ...
 4.3.68: ARCHITECTURE A semielliptical arch over a tunnel for a oneway road...
 4.3.69: ARCHITECTURE Repeat Exercise 68 for a semielliptical arch with a ma...
 4.3.70: GEOMETRY A line segment through a focus of an ellipse with endpoint...
 4.3.71: In Exercises 7174, sketch the graph of the ellipse, using the later...
 4.3.72: In Exercises 7174, sketch the graph of the ellipse, using the later...
 4.3.73: In Exercises 7174, sketch the graph of the ellipse, using the later...
 4.3.74: In Exercises 7174, sketch the graph of the ellipse, using the later...
 4.3.75: In Exercises 7584, find the center and vertices of the hyperbola an...
 4.3.76: In Exercises 7584, find the center and vertices of the hyperbola an...
 4.3.77: In Exercises 7584, find the center and vertices of the hyperbola an...
 4.3.78: In Exercises 7584, find the center and vertices of the hyperbola an...
 4.3.79: In Exercises 7584, find the center and vertices of the hyperbola an...
 4.3.80: In Exercises 7584, find the center and vertices of the hyperbola an...
 4.3.81: In Exercises 7584, find the center and vertices of the hyperbola an...
 4.3.82: In Exercises 7584, find the center and vertices of the hyperbola an...
 4.3.83: In Exercises 7584, find the center and vertices of the hyperbola an...
 4.3.84: In Exercises 7584, find the center and vertices of the hyperbola an...
 4.3.85: In Exercises 8592, find the standard form of the equation of the hy...
 4.3.86: In Exercises 8592, find the standard form of the equation of the hy...
 4.3.87: In Exercises 8592, find the standard form of the equation of the hy...
 4.3.88: In Exercises 8592, find the standard form of the equation of the hy...
 4.3.89: In Exercises 8592, find the standard form of the equation of the hy...
 4.3.90: In Exercises 8592, find the standard form of the equation of the hy...
 4.3.91: In Exercises 8592, find the standard form of the equation of the hy...
 4.3.92: In Exercises 8592, find the standard form of the equation of the hy...
 4.3.93: ART A sculpture has a hyperbolic cross section (see figure). (a) Wr...
 4.3.94: OPTICS A hyperbolic mirror (used in some telescopes) has the proper...
 4.3.95: AERONAUTICS When an airplane travels faster than the speed of sound...
 4.3.96: NAVIGATION Long distance radio navigation for aircraft and ships us...
 4.3.97: TRUE OR FALSE? In Exercises 97100, determine whether the statement ...
 4.3.98: TRUE OR FALSE? In Exercises 97100, determine whether the statement ...
 4.3.99: TRUE OR FALSE? In Exercises 97100, determine whether the statement ...
 4.3.100: TRUE OR FALSE? In Exercises 97100, determine whether the statement ...
 4.3.101: Consider the ellipse (a) The area of the ellipse is given by Write ...
 4.3.102: CAPSTONE Identify the conic. Explain your reasoning. (a) (b) (c) (d...
 4.3.103: THINK ABOUT IT How can you tell if an ellipse is a circle from the ...
 4.3.104: THINK ABOUT IT Is the graph of an ellipse? Explain.
 4.3.105: THINK ABOUT IT The graph of is a degenerate conic. Sketch this grap...
 4.3.106: THINK ABOUT IT Which part of the graph of the ellipse is represente...
 4.3.107: WRITING At the beginning of this section, you learned that each typ...
 4.3.108: WRITING Write a paragraph discussing the changes in the shape and o...
 4.3.109: Use the definition of an ellipse to derive the standard form of the...
 4.3.110: Use the definition of a hyperbola to derive the standard form of th...
 4.3.111: An ellipse can be drawn using two thumbtacks placed at the foci of ...
Solutions for Chapter 4.3: CONICS
Full solutions for College Algebra  8th Edition
ISBN: 9781439048696
Solutions for Chapter 4.3: CONICS
Get Full SolutionsThis textbook survival guide was created for the textbook: College Algebra , edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 4.3: CONICS includes 111 full stepbystep solutions. Since 111 problems in chapter 4.3: CONICS have been answered, more than 11830 students have viewed full stepbystep solutions from this chapter. College Algebra was written by Patricia and is associated to the ISBN: 9781439048696.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

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

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

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

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.

Iterative method.
A sequence of steps intended to approach the desired solution.

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.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

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.

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.

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

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

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

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

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

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.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.