 10.4.74E: Deriving polar equations for conies Modify Figure 10.55 to derive t...
 10.4.87AE: Equidistant set Show that the set of points equidistant from a circ...
 10.4.88AE: Polar equation of a conic Show that the polar equation of an ellips...
 10.4.1E: Give the property that defines all parabolas.
 10.4.2E: Give the property that defines all ellipses.
 10.4.3E: Give the property that defines all hyperbolas.
 10.4.4E: Sketch the three basic conic sections in standard position with ver...
 10.4.5E: Sketch the three basic conic sections in standard position with ver...
 10.4.6E: What is the equation of the standard parabola with its vertex at th...
 10.4.7E: What is the equation of the standard ellipse with vertices at (±a, ...
 10.4.8E: What is the equation of the standard hyperbola with vertices at (0,...
 10.4.9E: Given the vertices (±a, 0) and the eccentricity e, what are the coo...
 10.4.10E: Give the equation in polar coordinates of a conic section with a fo...
 10.4.11E: What are the equations of the asymptotes of a standard hyperbola wi...
 10.4.12E: How does the eccentricity determine the type of conic section?
 10.4.13E: Graphing parabolas Sketch the graph of the following parabolas. Spe...
 10.4.14E: Graphing parabolas Sketch the graph of the following parabolas. Spe...
 10.4.15E: Graphing parabolas Sketch the graph of the following parabolas. Spe...
 10.4.16E: Graphing parabolas Sketch the graph of the following parabolas. Spe...
 10.4.17E: Graphing parabolas Sketch the graph of the following parabolas. Spe...
 10.4.18E: Graphing parabolas Sketch the graph of the following parabolas. Spe...
 10.4.19E: Equations of parabolas Find an equation of the following parabolas,...
 10.4.20E: Equations of parabolas Find an equation of the following parabolas,...
 10.4.21E: Equations of parabolas Find an equation of the following parabolas,...
 10.4.22E: Equations of parabolas Find an equation of the following parabolas,...
 10.4.23E: Equations of parabolas Find an equation of the following parabolas,...
 10.4.24E: Equations of parabolas Find an equation of the following parabolas,...
 10.4.25E: From graphs to equations Write an equation of the following parabolas.
 10.4.26E: From graphs to equations Write an equation of the following parabolas.
 10.4.27E: Graphing ellipses Sketch the graph of the following ellipses. Plot ...
 10.4.28E: Graphing ellipses Sketch the graph of the following ellipses. Plot ...
 10.4.29E: Graphing ellipses Sketch the graph of the following ellipses. Plot ...
 10.4.30E: Graphing ellipses Sketch the graph of the following ellipses. Plot ...
 10.4.31E: Graphing ellipses Sketch the graph of the following ellipses. Plot ...
 10.4.32E: Graphing ellipses Sketch the graph of the following ellipses. Plot ...
 10.4.33E: Equations of ellipses Find an equation of the following ellipses, a...
 10.4.34E: Equations of ellipses Find an equation of the following ellipses, a...
 10.4.35E: Equations of ellipses Find an equation of the following ellipses, a...
 10.4.36E: Equations of ellipses Find an equation of the following ellipses, a...
 10.4.37E: From graphs to equations Write an equation of the following ellipses.
 10.4.38E: From graphs to equations Write an equation of the following ellipses.
 10.4.39E: Graphing hyperbolas Sketch the graph of the following hyperbolas. S...
 10.4.40E: Graphing hyperbolas Sketch the graph of the following hyperbolas. S...
 10.4.41E: Graphing hyperbolas Sketch the graph of the following hyperbolas. S...
 10.4.42E: Graphing hyperbolas Sketch the graph of the following hyperbolas. S...
 10.4.43E: Graphing hyperbolas Sketch the graph of the following hyperbolas. S...
 10.4.44E: Graphing hyperbolas Sketch the graph of the following hyperbolas. S...
 10.4.45E: Equations of hyperbolas Find an equation of the following hyperbola...
 10.4.46E: Equations of hyperbolas Find an equation of the following hyperbola...
 10.4.47E: Equations of hyperbolas Find an equation of the following hyperbola...
 10.4.48E: Equations of hyperbolas Find an equation of the following hyperbola...
 10.4.49E: From graphs to equations Write an equation of the following hyperbo...
 10.4.50E: From graphs to equations Write an equation of the following hyperbo...
 10.4.51E: Eccentricitydirectrix approach Find an equation of the following c...
 10.4.52E: Eccentricitydirectrix approach Find an equation of the following c...
 10.4.53E: Eccentricitydirectrix approach Find an equation of the following c...
 10.4.54E: Eccentricitydirectrix approach Find an equation of the following c...
 10.4.55E: Polar equations for conic sections Graph the following conic sectio...
 10.4.56E: Polar equations for conic sections Graph the following conic sectio...
 10.4.57E: Polar equations for conic sections Graph the following conic sectio...
 10.4.58E: Polar equations for conic sections Graph the following conic sectio...
 10.4.59E: Polar equations for conic sections Graph the following conic sectio...
 10.4.60E: Polar equations for conic sections Graph the following conic sectio...
 10.4.61E: Tracing hyperbolas and parabolas Graph the following equations. The...
 10.4.62E: Tracing hyperbolas and parabolas Graph the following equations. The...
 10.4.63E: Tracing hyperbolas and parabolas Graph the following equations. The...
 10.4.64E: Tracing hyperbolas and parabolas Graph the following equations. The...
 10.4.65E: Parabolas with a graphing utility Use a graphing utility to graph t...
 10.4.66E: Hyperbolas with a graphing utility Use a graphing utility to graph ...
 10.4.67E: Explain why or why not Determine whether the following statements a...
 10.4.68E: Tangent lines Find an equation of the line tangent to the following...
 10.4.69E: Tangent lines Find an equation of the line tangent to the following...
 10.4.70E: Tangent lines Find an equation of the line tangent to the following...
 10.4.71E: Tangent lines Find an equation of the line tangent to the following...
 10.4.72E: Graphs to polar equations Find a polar equation for each conic sect...
 10.4.73E: Graphs to polar equations Find a polar equation for each conic sect...
 10.4.75E: Another construction for a hyperbola Suppose two circles are center...
 10.4.76E: The ellipse and the parabola Let R be the region bounded by the upp...
 10.4.77E: Tangent lines for an ellipse Show that an equation of the line tang...
 10.4.78E: Tangent lines for a hyperbola Find an equation of the line tangent ...
 10.4.79E: Volume of an ellipsoid Suppose that the ellipse x2/a2 + y2/b2 = 1 i...
 10.4.80E: Area of a sector of a hyperbola Consider the region R bounded by th...
 10.4.81E: Volume of a hyperbolic cap Consider the region R bounded by the rig...
 10.4.82E: Volume of a paraboloid (Archimedes) The region bounded b the parabo...
 10.4.83E: (See the Guided Projects for additional applications of conic secti...
 10.4.84E: (See the Guided Projects for additional applications of conic secti...
 10.4.85AE: Equation of an ellipse Consider an ellipse to be the set of points ...
 10.4.86AE: Equation of a hyperbola Consider a hyperbola to be the set of point...
 10.4.89AE: Shared asymptotes Suppose that two hyperbolas with eccentricities e...
 10.4.90AE: Focal chords A focal chord of a conic section is a line through a f...
 10.4.91AE: Focal chords A focal chord of a conic section is a line through a f...
 10.4.92AE: Focal chords A focal chord of a conic section is a line through a f...
 10.4.93AE: Focal chords A focal chord of a conic section is a line through a f...
 10.4.94AE: Focal chords A focal chord of a conic section is a line through a f...
 10.4.95AE: Confocal ellipse and hyperbola Show that an ellipse and a hyperbola...
 10.4.96AE: Approach to asymptotes Show that the vertical distance between a hy...
 10.4.97AE: Sector of a hyperbola Let H be the right branch of the hyperbola x2...
 10.4.98AE: The anvil of a hyperbola Let H be the hyperbola x2 ? y2 = 1 and let...
 10.4.99AE: Parametric equations for an ellipse Consider the parametric equatio...
Solutions for Chapter 10.4: Calculus: Early Transcendentals 1st Edition
Full solutions for Calculus: Early Transcendentals  1st Edition
ISBN: 9780321570567
Solutions for Chapter 10.4
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 10.4 includes 99 full stepbystep solutions. Since 99 problems in chapter 10.4 have been answered, more than 222718 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

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

Base
See Exponential function, Logarithmic function, nth power of a.

Cotangent
The function y = cot x

Data
Facts collected for statistical purposes (singular form is datum)

Dependent variable
Variable representing the range value of a function (usually y)

Equilibrium price
See Equilibrium point.

Extracting square roots
A method for solving equations in the form x 2 = k.

Linear factorization theorem
A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1  z1) 1x  i z 22 Á 1x  z n where the z1 are the zeros of ƒ

Midpoint (in Cartesian space)
For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b

Multiplicative inverse of a matrix
See Inverse of a matrix

Multiplicity
The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x  c) (x  z 2) Á (x  z n)

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Obtuse triangle
A triangle in which one angle is greater than 90°.

Power rule of logarithms
logb Rc = c logb R, R 7 0.

Probability simulation
A numerical simulation of a probability experiment in which assigned numbers appear with the same probabilities as the outcomes of the experiment.

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Quartile
The first quartile is the median of the lower half of a set of data, the second quartile is the median, and the third quartile is the median of the upper half of the data.

Real zeros
Zeros of a function that are real numbers.

Repeated zeros
Zeros of multiplicity ? 2 (see Multiplicity).

Transformation
A function that maps real numbers to real numbers.