 8.5.8.1.1.338: In Exercises 1 and 2, solve for r.13, u2 = 1r, u + p2
 8.5.8.1.1.339: In Exercises 1 and 2, solve for r.12, u2 = 1r, u + p2
 8.5.8.1.1.340: In Exercises 3 and 4, solve for .11.5, p/62 = 11.5, u2, 2p u 2p
 8.5.8.1.1.341: In Exercises 3 and 4, solve for .13, 4p/32 = 13, u2, 2p u 2p
 8.5.8.1.1.342: In Exercises 5 and 6, find the focus and directrix of the parabola....
 8.5.8.1.1.343: In Exercises 5 and 6, find the focus and directrix of the parabola....
 8.5.8.1.1.344: In Exercises 710, find the foci and vertices of the conic.x 2 9 + y...
 8.5.8.1.1.345: In Exercises 710, find the foci and vertices of the conic.y2 25 + x...
 8.5.8.1.1.346: In Exercises 710, find the foci and vertices of the conic.x 2 16  ...
 8.5.8.1.1.347: In Exercises 710, find the foci and vertices of the conic. y2 36  ...
 8.5.8.1.1.348: In Exercises 16, find a polar equation for the conic with a focus a...
 8.5.8.1.1.349: In Exercises 16, find a polar equation for the conic with a focus a...
 8.5.8.1.1.350: In Exercises 16, find a polar equation for the conic with a focus a...
 8.5.8.1.1.351: In Exercises 16, find a polar equation for the conic with a focus a...
 8.5.8.1.1.352: In Exercises 16, find a polar equation for the conic with a focus a...
 8.5.8.1.1.353: In Exercises 16, find a polar equation for the conic with a focus a...
 8.5.8.1.1.354: In Exercises 714, determine the eccentricity, type of conic, and di...
 8.5.8.1.1.355: In Exercises 714, determine the eccentricity, type of conic, and di...
 8.5.8.1.1.356: In Exercises 714, determine the eccentricity, type of conic, and di...
 8.5.8.1.1.357: In Exercises 714, determine the eccentricity, type of conic, and di...
 8.5.8.1.1.358: In Exercises 714, determine the eccentricity, type of conic, and di...
 8.5.8.1.1.359: In Exercises 714, determine the eccentricity, type of conic, and di...
 8.5.8.1.1.360: In Exercises 714, determine the eccentricity, type of conic, and di...
 8.5.8.1.1.361: In Exercises 714, determine the eccentricity, type of conic, and di...
 8.5.8.1.1.362: In Exercises 1520, match the polar equation with its graph, and ide...
 8.5.8.1.1.363: In Exercises 1520, match the polar equation with its graph, and ide...
 8.5.8.1.1.364: In Exercises 1520, match the polar equation with its graph, and ide...
 8.5.8.1.1.365: In Exercises 1520, match the polar equation with its graph, and ide...
 8.5.8.1.1.366: In Exercises 1520, match the polar equation with its graph, and ide...
 8.5.8.1.1.367: In Exercises 1520, match the polar equation with its graph, and ide...
 8.5.8.1.1.368: In Exercises 2124, find a polar equation for the ellipse with a foc...
 8.5.8.1.1.369: In Exercises 2124, find a polar equation for the ellipse with a foc...
 8.5.8.1.1.370: In Exercises 2124, find a polar equation for the ellipse with a foc...
 8.5.8.1.1.371: In Exercises 2124, find a polar equation for the ellipse with a foc...
 8.5.8.1.1.372: In Exercises 2528, find a polar equation for the hyperbola with a f...
 8.5.8.1.1.373: In Exercises 2528, find a polar equation for the hyperbola with a f...
 8.5.8.1.1.374: In Exercises 2528, find a polar equation for the hyperbola with a f...
 8.5.8.1.1.375: In Exercises 2528, find a polar equation for the hyperbola with a f...
 8.5.8.1.1.376: In Exercises 29 and 30, find a polar equation for the conic with a ...
 8.5.8.1.1.377: In Exercises 29 and 30, find a polar equation for the conic with a ...
 8.5.8.1.1.378: In Exercises 3136, graph the conic, and find the values of e, a, b,...
 8.5.8.1.1.379: In Exercises 3136, graph the conic, and find the values of e, a, b,...
 8.5.8.1.1.380: In Exercises 3136, graph the conic, and find the values of e, a, b,...
 8.5.8.1.1.381: In Exercises 3136, graph the conic, and find the values of e, a, b,...
 8.5.8.1.1.382: In Exercises 3136, graph the conic, and find the values of e, a, b,...
 8.5.8.1.1.383: In Exercises 3136, graph the conic, and find the values of e, a, b,...
 8.5.8.1.1.384: In Exercises 37 and 38, determine a Cartesian equation for the give...
 8.5.8.1.1.385: In Exercises 37 and 38, determine a Cartesian equation for the give...
 8.5.8.1.1.386: In Exercises 39 and 40, use the fact that is twice the focal length...
 8.5.8.1.1.387: In Exercises 39 and 40, use the fact that is twice the focal length...
 8.5.8.1.1.388: Halleys Comet The orbit of Halleys comet has a semimajor axis of 18...
 8.5.8.1.1.389: Uranus The orbit of the planet Uranus has a semimajor axis of 19.18...
 8.5.8.1.1.390: In Exercises 43 and 44, the velocity of an object traveling in a ci...
 8.5.8.1.1.391: In Exercises 43 and 44, the velocity of an object traveling in a ci...
 8.5.8.1.1.392: True or False The equation yields no true circles. Justify your ans...
 8.5.8.1.1.393: True or False The equation yields no true parabolas. Justify your a...
 8.5.8.1.1.394: Which ratio of distances is constant for a point on a nondegenerate...
 8.5.8.1.1.395: Which type of conic section has an eccentricity greater than one? (...
 8.5.8.1.1.396: For a conic expressed by , which point is located at the pole? (A) ...
 8.5.8.1.1.397: Which of the following is not a polar equation of a conic? (A) (B) ...
 8.5.8.1.1.398: Planetary Orbits Use the polar equation in completing the following...
 8.5.8.1.1.399: Using the Astronomers Equation for Conics Using Dot mode, , an xy w...
 8.5.8.1.1.400: Revisiting Figure 8.41 In Figure 8.41, if or then we must use Prove...
 8.5.8.1.1.401: Deriving Other Polar Forms for Conics Using Figure 8.41 as a guide,...
 8.5.8.1.1.402: Revisiting Example 3 Use the formulas and to transform the polar eq...
 8.5.8.1.1.403: Focal Widths Using polar equations, derive formulas for the focal w...
 8.5.8.1.1.404: Prove that for a hyperbola the formula is equivalent to where a is ...
 8.5.8.1.1.405: Connecting Polar to Rectangular Consider the ellipse where half the...
 8.5.8.1.1.406: Connecting Polar to Rectangular Consider the hyperbola where half t...
Solutions for Chapter 8.5: Analytic Geometry in Two and Three Dimensions
Full solutions for Precalculus: Graphical, Numerical, Algebraic  8th Edition
ISBN: 9780321656933
Solutions for Chapter 8.5: Analytic Geometry in Two and Three Dimensions
Get Full SolutionsChapter 8.5: Analytic Geometry in Two and Three Dimensions includes 69 full stepbystep solutions. Precalculus: Graphical, Numerical, Algebraic was written by and is associated to the ISBN: 9780321656933. Since 69 problems in chapter 8.5: Analytic Geometry in Two and Three Dimensions have been answered, more than 45608 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Precalculus: Graphical, Numerical, Algebraic, edition: 8th Edition.

Acute angle
An angle whose measure is between 0° and 90°

Conjugate axis of a hyperbola
The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

Difference of two vectors
<u1, u2>  <v1, v2> = <u1  v1, u2  v2> or <u1, u2, u3>  <v1, v2, v3> = <u1  v1, u2  v2, u3  v3>

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Expanded form
The right side of u(v + w) = uv + uw.

Exponential form
An equation written with exponents instead of logarithms.

First quartile
See Quartile.

Horizontal asymptote
The line is a horizontal asymptote of the graph of a function ƒ if lim x: q ƒ(x) = or lim x: q ƒ(x) = b

Hypotenuse
Side opposite the right angle in a right triangle.

Infinite discontinuity at x = a
limx:a + x a ƒ(x) = q6 or limx:a  ƒ(x) = q.

Limit to growth
See Logistic growth function.

Multiplication property of inequality
If u < v and c > 0, then uc < vc. If u < and c < 0, then uc > vc

Natural numbers
The numbers 1, 2, 3, . . . ,.

Perpendicular lines
Two lines that are at right angles to each other

Pole
See Polar coordinate system.

Projectile motion
The movement of an object that is subject only to the force of gravity

Riemann sum
A sum where the interval is divided into n subintervals of equal length and is in the ith subinterval.

Scalar
A real number.

Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt

Zero factor property
If ab = 0 , then either a = 0 or b = 0.