 7.1: Determine whether the statement is true or false. The graph of x + ...
 7.2: Determine whether the statement is true or false. The graph of1x  ...
 7.3: Determine whether the statement is true or false. The hyperbolax25...
 7.4: Determine whether the statement is true or false. Every nonlinear s...
 7.5: Determine whether the statement is true or false. The graph of a no...
 7.6: In Exercises 613, match the equation with one of thegraphs (a)(h), ...
 7.7: In Exercises 613, match the equation with one of thegraphs (a)(h), ...
 7.8: In Exercises 613, match the equation with one of thegraphs (a)(h), ...
 7.9: In Exercises 613, match the equation with one of thegraphs (a)(h), ...
 7.10: In Exercises 613, match the equation with one of thegraphs (a)(h), ...
 7.11: In Exercises 613, match the equation with one of thegraphs (a)(h), ...
 7.12: In Exercises 613, match the equation with one of thegraphs (a)(h), ...
 7.13: In Exercises 613, match the equation with one of thegraphs (a)(h), ...
 7.14: Find an equation of the parabola with directrixy = 32and focus 10, ...
 7.15: Find the focus, the vertex, and the directrix of theparabola given ...
 7.16: Find the vertex, the focus, and the directrix of theparabola given ...
 7.17: Find the center, the vertices, and the foci of theellipse given by1...
 7.18: Find an equation of the ellipse having vertices10, 42 and 10, 42 w...
 7.19: Find the center, the vertices, the foci, and theasymptotes of the h...
 7.20: Spotlight. A spotlight has a parabolic crosssection that is 2 ft wi...
 7.21: Solve. x2  16y = 0,x2  y2 = 64
 7.22: Solve. 4x2 + 4y2 = 65,6x2  4y2 = 25
 7.23: Solve. x2  y2 = 33,x + y = 11
 7.24: Solve.x2  2x + 2y2 = 8,2x + y = 6
 7.25: Solve.x2  y = 3,2x  y = 3
 7.26: Solve.x2 + y2 = 25,x2  y2 = 7
 7.27: Solve.x2  y2 = 3,y = x2  3
 7.28: Solve.x2 + y2 = 18,2x + y = 3
 7.29: Solve.x2 + y2 = 100,2x2  3y2 = 120
 7.30: Solve.x2 + 2y2 = 12,xy = 4
 7.31: Numerical Relationship. The sum of two numbersis 11, and the sum of...
 7.32: Dimensions of a Rectangle. A rectangle has aperimeter of 38 m and a...
 7.33: Numerical Relationship. Find two positive integerswhose sum is 12 a...
 7.34: Perimeter. The perimeter of a square is 12 cmmore than the perimete...
 7.35: Radius of a Circle. The sum of the areas of twocircles is 130p ft2....
 7.36: Graph the system of inequalities. Then find the coordinatesof the p...
 7.37: Graph the system of inequalities. Then find the coordinatesof the p...
 7.38: Graph the system of inequalities. Then find the coordinatesof the p...
 7.39: Graph the system of inequalities. Then find the coordinatesof the p...
 7.40: The vertex of the parabola y2  4y  12x  8 = 0is which of the fol...
 7.41: Which of the following cannot be a number ofsolutions possible for ...
 7.42: The graph of x2 + 4y2 = 4 is which of thefollowing?
 7.43: Find two numbers whose product is 4 and thesum of whose reciprocals...
 7.44: Find an equation of the circle that passesthrough the points 110, 7...
 7.45: Find an equation of the ellipse containing thepoint 11>2, 323>22 a...
 7.46: Navigation. Two radio transmitters positioned400 mi apart along the...
 7.47: Is a circle a special type of ellipse? Why or whynot?
 7.48: How does the graph of a parabola differ from thegraph of one branch...
 7.49: Are the asymptotes of a hyperbola part of the graphof the hyperbola...
 7.50: What would you say to a classmate who tells youthat it is always po...
Solutions for Chapter 7: Conic Sections
Full solutions for College Algebra: Graphs and Models  5th Edition
ISBN: 9780321783950
Solutions for Chapter 7: Conic Sections
Get Full SolutionsCollege Algebra: Graphs and Models was written by and is associated to the ISBN: 9780321783950. This textbook survival guide was created for the textbook: College Algebra: Graphs and Models, edition: 5. Chapter 7: Conic Sections includes 50 full stepbystep solutions. Since 50 problems in chapter 7: Conic Sections have been answered, more than 27501 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

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

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

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

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.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

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

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

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 equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

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

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

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

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.