 7.3.1: The set of all points in a plane that are equidistant from a fixed ...
 7.3.2: Use the graph shown to answer Exercises 25. y x 2. The equation of ...
 7.3.3: If 4p = 28, then the coordinates of the focus are .
 7.3.4: If 4p = 28, then the equation of the directrix is .
 7.3.5: If 4p = 28, then the length of the latus rectum is . The endpoints...
 7.3.6: Use the graph shown to answer Exercises 69. y x (2, 1) 6. The equat...
 7.3.7: If 4p = 4, then the coordinates of the focus are .
 7.3.8: If 4p = 4, then the equation of the directrix is .
 7.3.9: If 4p = 4, then the length of the latus rectum is . The endpoints o...
 7.3.10: A nondegenerate conic section in the form Ax2 + Cy2 + Dx + Ey + F =...
 7.3.11: In Exercises 516, find the focus and directrix of the parabola with...
 7.3.12: In Exercises 516, find the focus and directrix of the parabola with...
 7.3.13: In Exercises 516, find the focus and directrix of the parabola with...
 7.3.14: In Exercises 516, find the focus and directrix of the parabola with...
 7.3.15: In Exercises 516, find the focus and directrix of the parabola with...
 7.3.16: In Exercises 516, find the focus and directrix of the parabola with...
 7.3.17: In Exercises 1730, find the standard form of the equation of each p...
 7.3.18: In Exercises 1730, find the standard form of the equation of each p...
 7.3.19: In Exercises 1730, find the standard form of the equation of each p...
 7.3.20: In Exercises 1730, find the standard form of the equation of each p...
 7.3.21: In Exercises 1730, find the standard form of the equation of each p...
 7.3.22: In Exercises 1730, find the standard form of the equation of each p...
 7.3.23: In Exercises 1730, find the standard form of the equation of each p...
 7.3.24: In Exercises 1730, find the standard form of the equation of each p...
 7.3.25: In Exercises 1730, find the standard form of the equation of each p...
 7.3.26: In Exercises 1730, find the standard form of the equation of each p...
 7.3.27: In Exercises 1730, find the standard form of the equation of each p...
 7.3.28: In Exercises 1730, find the standard form of the equation of each p...
 7.3.29: In Exercises 1730, find the standard form of the equation of each p...
 7.3.30: In Exercises 1730, find the standard form of the equation of each p...
 7.3.31: In Exercises 3134, find the vertex, focus, and directrix of each pa...
 7.3.32: In Exercises 3134, find the vertex, focus, and directrix of each pa...
 7.3.33: In Exercises 3134, find the vertex, focus, and directrix of each pa...
 7.3.34: In Exercises 3134, find the vertex, focus, and directrix of each pa...
 7.3.35: In Exercises 3542, find the vertex, focus, and directrix of each pa...
 7.3.36: In Exercises 3542, find the vertex, focus, and directrix of each pa...
 7.3.37: In Exercises 3542, find the vertex, focus, and directrix of each pa...
 7.3.38: In Exercises 3542, find the vertex, focus, and directrix of each pa...
 7.3.39: In Exercises 3542, find the vertex, focus, and directrix of each pa...
 7.3.40: In Exercises 3542, find the vertex, focus, and directrix of each pa...
 7.3.41: In Exercises 3542, find the vertex, focus, and directrix of each pa...
 7.3.42: In Exercises 3542, find the vertex, focus, and directrix of each pa...
 7.3.43: In Exercises 4348, convert each equation to standard form by comple...
 7.3.44: In Exercises 4348, convert each equation to standard form by comple...
 7.3.45: In Exercises 4348, convert each equation to standard form by comple...
 7.3.46: In Exercises 4348, convert each equation to standard form by comple...
 7.3.47: In Exercises 4348, convert each equation to standard form by comple...
 7.3.48: In Exercises 4348, convert each equation to standard form by comple...
 7.3.49: In Exercises 4956, identify each equation without completing the sq...
 7.3.50: In Exercises 4956, identify each equation without completing the sq...
 7.3.51: In Exercises 4956, identify each equation without completing the sq...
 7.3.52: In Exercises 4956, identify each equation without completing the sq...
 7.3.53: In Exercises 4956, identify each equation without completing the sq...
 7.3.54: In Exercises 4956, identify each equation without completing the sq...
 7.3.55: In Exercises 4956, identify each equation without completing the sq...
 7.3.56: In Exercises 4956, identify each equation without completing the sq...
 7.3.57: In Exercises 5762, use the vertex and the direction in which the pa...
 7.3.58: In Exercises 5762, use the vertex and the direction in which the pa...
 7.3.59: In Exercises 5762, use the vertex and the direction in which the pa...
 7.3.60: In Exercises 5762, use the vertex and the direction in which the pa...
 7.3.61: In Exercises 5762, use the vertex and the direction in which the pa...
 7.3.62: In Exercises 5762, use the vertex and the direction in which the pa...
 7.3.63: In Exercises 6368, find the solution set for each system by graphin...
 7.3.64: In Exercises 6368, find the solution set for each system by graphin...
 7.3.65: In Exercises 6368, find the solution set for each system by graphin...
 7.3.66: In Exercises 6368, find the solution set for each system by graphin...
 7.3.67: In Exercises 6368, find the solution set for each system by graphin...
 7.3.68: In Exercises 6368, find the solution set for each system by graphin...
 7.3.69: The reflector of a flashlight is in the shape of a parabolic surfac...
 7.3.70: The reflector of a flashlight is in the shape of a parabolic surfac...
 7.3.71: A satellite dish, like the one shown below, is in the shape of a pa...
 7.3.72: In Exercise 71, if the diameter of the dish is halved and the depth...
 7.3.73: The towers of the Golden Gate Bridge connecting San Francisco to Ma...
 7.3.74: The towers of a suspension bridge are 800 feet apart and rise 160 f...
 7.3.75: The parabolic arch shown in the figure is 50 feet above the water a...
 7.3.76: A satellite dish in the shape of a parabolic surface has a diameter...
 7.3.77: What is a parabola?
 7.3.78: Explain how to use y2 = 8x to find the parabolas focus and directrix
 7.3.79: If you are given the standard form of the equation of a parabola wi...
 7.3.80: Describe one similarity and one difference between the graphs of y2...
 7.3.81: How can you distinguish parabolas from other conic sections by look...
 7.3.82: Look at the satellite dish shown in Exercise 71.Why must the receiv...
 7.3.83: Explain how to identify the graph of Ax2 + Cy2 + Dx + Ey + F = 0.
 7.3.84: Use a graphing utility to graph any five of the parabolas that you ...
 7.3.85: Use a graphing utility to graph any three of the parabolas that you...
 7.3.86: Use a graphing utility to graph the parabolas in Exercises 8687. Wr...
 7.3.87: Use a graphing utility to graph the parabolas in Exercises 8687. Wr...
 7.3.88: In Exercises 8889, write each equation as a quadratic equation in y...
 7.3.89: In Exercises 8889, write each equation as a quadratic equation in y...
 7.3.90: In Exercises 9093, determine whether each statement makes sense or ...
 7.3.91: Knowing that a parabola opening to the right has a vertex at (1, 1...
 7.3.92: I noticed that depending on the values for A and C, assuming that t...
 7.3.93: Im using a telescope in which light from distant stars is reflected...
 7.3.94: In Exercises 9497, determine whether each statement is true or fals...
 7.3.95: If the parabola whose equation is x = ay2 + by + c has its vertex a...
 7.3.96: Some parabolas that open to the right have equations that define y ...
 7.3.97: The graph of x = a(y  k) + h is a parabola with vertex at (h, k).
 7.3.98: Find the focus and directrix of a parabola whose equation is of the...
 7.3.99: Write the standard form of the equation of a parabola whose points ...
 7.3.100: Consult the research department of your library or the Internet to ...
 7.3.101: Solve the system: e y = x2  7 x2 + y2 = 13. (Section 5.4, Example 4)
 7.3.102: . Consider the system c x  y + z = 3 2y + z = 6 2x  3y = 10....
 7.3.103: Use Cramers Rule (determinants) to solve the system: e x  y = 5 3...
 7.3.104: Exercises 104106 will help you prepare for the material covered in ...
 7.3.105: Find the product of all positive integers from n down through 1 for...
 7.3.106: Evaluate i 2 + 1 for all consecutive integers from 1 to 6, inclusiv...
Solutions for Chapter 7.3: The Parabola
Full solutions for College Algebra  7th Edition
ISBN: 9780134469164
Solutions for Chapter 7.3: The Parabola
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 7.3: The Parabola includes 106 full stepbystep solutions. This textbook survival guide was created for the textbook: College Algebra , edition: 7. Since 106 problems in chapter 7.3: The Parabola have been answered, more than 32555 students have viewed full stepbystep solutions from this chapter. College Algebra was written by and is associated to the ISBN: 9780134469164.

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).

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.

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

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

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

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.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

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

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

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

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

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).

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).

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).

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.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

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