 10.2.1: The set of all points in a plane the sum of whose distances from tw...
 10.2.2: Consider the following equation in standard form: x2 25 + y2 9 = 1....
 10.2.3: Consider the following equation in standard form: x2 9 + y2 25 = 1....
 10.2.4: The graph of (x + 1) 2 25 + (y  4) 2 9 has its center at _________...
 10.2.5: If the center of an ellipse is (3, 2), the major axis is horizonta...
 10.2.6: In Exercises 116, graph each ellipse.x249+ y236 = 1
 10.2.7: In Exercises 116, graph each ellipse.x249+ y281 = 1
 10.2.8: In Exercises 116, graph each ellipse.x264+ y2100 = 1
 10.2.9: In Exercises 116, graph each ellipse.25x2 + 4y2 = 100
 10.2.10: In Exercises 116, graph each ellipse.9x2 + 4y2 = 36
 10.2.11: In Exercises 116, graph each ellipse.4x2 + 16y2 = 64
 10.2.12: In Exercises 116, graph each ellipse.16x2 + 9y2 = 144
 10.2.13: In Exercises 116, graph each ellipse.25x2 + 9y2 = 225
 10.2.14: In Exercises 116, graph each ellipse.4x2 + 25y2 = 100
 10.2.15: In Exercises 116, graph each ellipse.x2 + 2y2 = 8
 10.2.16: In Exercises 116, graph each ellipse.12x2 + 4y2 = 36
 10.2.17: In Exercises 1720, find the standard form of the equation of each e...
 10.2.18: In Exercises 1720, find the standard form of the equation of each e...
 10.2.19: In Exercises 1720, find the standard form of the equation of each e...
 10.2.20: In Exercises 1720, find the standard form of the equation of each e...
 10.2.21: In Exercises 2132, graph each ellipse.(x  2)29+ (y  1)24 = 1
 10.2.22: In Exercises 2132, graph each ellipse.(x  1)216+ (y + 2)29 = 1
 10.2.23: In Exercises 2132, graph each ellipse.(x + 3)2 + 4(y  2)2 = 16
 10.2.24: In Exercises 2132, graph each ellipse.. (x  3)2 + 9(y + 2)2 = 36
 10.2.25: In Exercises 2132, graph each ellipse.(x  4)29+ (y + 2)225 = 1
 10.2.26: In Exercises 2132, graph each ellipse.(x  3)29+ (y + 1)216 = 1
 10.2.27: In Exercises 2132, graph each ellipse.x225+ (y  2)236 = 1
 10.2.28: In Exercises 2132, graph each ellipse.(x  4)24+ y225 = 1
 10.2.29: In Exercises 2132, graph each ellipse.(x + 3)29+ (y  2)2 = 1
 10.2.30: In Exercises 2132, graph each ellipse.(x + 2)216+ (y  3)2 = 1
 10.2.31: In Exercises 2132, graph each ellipse.9(x  1)2 + 4(y + 3)2 = 36
 10.2.32: In Exercises 2132, graph each ellipse.36(x + 4)2 + (y + 3)2 = 36
 10.2.33: In Exercises 3334, find the standard form of the equation of each e...
 10.2.34: In Exercises 3334, find the standard form of the equation of each e...
 10.2.35: In Exercises 3540, find the solution set for each system by graphin...
 10.2.36: In Exercises 3540, find the solution set for each system by graphin...
 10.2.37: In Exercises 3540, find the solution set for each system by graphin...
 10.2.38: In Exercises 3540, find the solution set for each system by graphin...
 10.2.39: In Exercises 3540, find the solution set for each system by graphin...
 10.2.40: In Exercises 3540, find the solution set for each system by graphin...
 10.2.41: In Exercises 4142, graph each semiellipse.y =  216  4x2
 10.2.42: In Exercises 4142, graph each semiellipse.y =  24  4x2
 10.2.43: Will a truck that is 8 feet wide carrying a load that reaches 7 fee...
 10.2.44: A semielliptic archway has a height of 20 feet and a width of 50 fe...
 10.2.45: The elliptical ceiling in Statuary Hall in the U.S. Capitol Buildin...
 10.2.46: If an elliptical whispering room has a height of 30 feet and a widt...
 10.2.47: What is an ellipse?
 10.2.48: Describe how to graph x2 25 + y2 16 = 1.
 10.2.49: Describe one similarity and one difference between the graphs of x2...
 10.2.50: Describe one similarity and one difference between the graphs of x2...
 10.2.51: An elliptipool is an elliptical pool table with only one pocket. A ...
 10.2.52: Use a graphing utility to graph any five of the ellipses that you g...
 10.2.53: Use a graphing utility to graph any three of the ellipses that you ...
 10.2.54: Make Sense? In Exercises 5457, determine whether each statement mak...
 10.2.55: Make Sense? In Exercises 5457, determine whether each statement mak...
 10.2.56: Make Sense? In Exercises 5457, determine whether each statement mak...
 10.2.57: Make Sense? In Exercises 5457, determine whether each statement mak...
 10.2.58: In Exercises 5861, determine whether each statement is true or fals...
 10.2.59: In Exercises 5861, determine whether each statement is true or fals...
 10.2.60: In Exercises 5861, determine whether each statement is true or fals...
 10.2.61: In Exercises 5861, determine whether each statement is true or fals...
 10.2.62: Find the standard form of the equation of an ellipse with vertices ...
 10.2.63: In Exercises 6364, convert each equation to standard form by comple...
 10.2.64: In Exercises 6364, convert each equation to standard form by comple...
 10.2.65: An Earth satellite has an elliptical orbit described by x2 (5000) 2...
 10.2.66: The equation of the red ellipse in the figure shown is x2 25 + y2 9...
 10.2.67: Factor completely: x3 + 2x2  4x  8. (Section 5.5, Example 4)
 10.2.68: Simplify: 3 240x4y7 . (Section 7.3, Example 5)
 10.2.69: Solve: 2 x + 2 + 4 x  2 = x  1 x2  4 . (Section 6.6, Example 5)
 10.2.70: Exercises 7072 will help you prepare for the material covered in th...
 10.2.71: Exercises 7072 will help you prepare for the material covered in th...
 10.2.72: Exercises 7072 will help you prepare for the material covered in th...
Solutions for Chapter 10.2: The Ellipse
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 10.2: The Ellipse
Get Full SolutionsSince 72 problems in chapter 10.2: The Ellipse have been answered, more than 20391 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 10.2: The Ellipse includes 72 full stepbystep solutions. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

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

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

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.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

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.

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

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

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.

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).

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.