 11.5.1: Decide if the equation defines an ellipse, a hyperbola, a parabola,...
 11.5.2: For which conic sections do the vertices lie between the foci?
 11.5.3: What are the foci of x a 2 + y b 2 = 1 if a
 11.5.4: What is the geometric interpretation of b/a in the equation of a hy...
 11.5.5: In Exercises 16, find the vertices and foci of the conic section.x ...
 11.5.6: In Exercises 16, find the vertices and foci of the conic section.x ...
 11.5.7: In Exercises 710, find the equation of the ellipse obtained by tran...
 11.5.8: In Exercises 710, find the equation of the ellipse obtained by tran...
 11.5.9: In Exercises 710, find the equation of the ellipse obtained by tran...
 11.5.10: In Exercises 710, find the equation of the ellipse obtained by tran...
 11.5.11: In Exercises 1114, find the equation of the given ellipse. Vertices...
 11.5.12: In Exercises 1114, find the equation of the given ellipse. (6, 0) a...
 11.5.13: In Exercises 1114, find the equation of the given ellipse. Foci (0,...
 11.5.14: In Exercises 1114, find the equation of the given ellipse. Vertices...
 11.5.15: In Exercises 1520, find the equation of the given hyperbola. Vertic...
 11.5.16: In Exercises 1520, find the equation of the given hyperbola. Vertic...
 11.5.17: In Exercises 1520, find the equation of the given hyperbola. Foci (...
 11.5.18: In Exercises 1520, find the equation of the given hyperbola. Vertic...
 11.5.19: In Exercises 1520, find the equation of the given hyperbola. Vertic...
 11.5.20: In Exercises 1520, find the equation of the given hyperbola. Vertic...
 11.5.21: In Exercises 2128, find the equation of the parabola with the given...
 11.5.22: In Exercises 2128, find the equation of the parabola with the given...
 11.5.23: In Exercises 2128, find the equation of the parabola with the given...
 11.5.24: In Exercises 2128, find the equation of the parabola with the given...
 11.5.25: In Exercises 2128, find the equation of the parabola with the given...
 11.5.26: In Exercises 2128, find the equation of the parabola with the given...
 11.5.27: In Exercises 2128, find the equation of the parabola with the given...
 11.5.28: In Exercises 2128, find the equation of the parabola with the given...
 11.5.29: In Exercises 2938, find the vertices, foci, center (if an ellipse o...
 11.5.30: In Exercises 2938, find the vertices, foci, center (if an ellipse o...
 11.5.31: In Exercises 2938, find the vertices, foci, center (if an ellipse o...
 11.5.32: In Exercises 2938, find the vertices, foci, center (if an ellipse o...
 11.5.33: In Exercises 2938, find the vertices, foci, center (if an ellipse o...
 11.5.34: In Exercises 2938, find the vertices, foci, center (if an ellipse o...
 11.5.35: In Exercises 2938, find the vertices, foci, center (if an ellipse o...
 11.5.36: In Exercises 2938, find the vertices, foci, center (if an ellipse o...
 11.5.37: In Exercises 2938, find the vertices, foci, center (if an ellipse o...
 11.5.38: In Exercises 2938, find the vertices, foci, center (if an ellipse o...
 11.5.39: In Exercises 3942, use the Discriminant Test to determine the type ...
 11.5.40: In Exercises 3942, use the Discriminant Test to determine the type ...
 11.5.41: In Exercises 3942, use the Discriminant Test to determine the type ...
 11.5.42: In Exercises 3942, use the Discriminant Test to determine the type ...
 11.5.43: Show that the conic x2 + 3y2 6x + 12y + 23 = 0 has no points.
 11.5.44: For which values of a does the conic 3x2 + 2y2 16y + 12x = a have a...
 11.5.45: Show that b a = 1 e2 for a standard ellipse of eccentricity e.
 11.5.46: Show that the eccentricity of a hyperbola in standard position is e...
 11.5.47: Explain why the dots in Figure 23 lie on a parabola. Where are the ...
 11.5.48: Find the equation of the ellipse consisting of points P such that P...
 11.5.49: A latus rectum of a conic section is a chord through a focus parall...
 11.5.50: Show that the tangent line at a point P = (x0, y0) on the hyperbola...
 11.5.51: In Exercises 5154, find the polar equation of the conic with the gi...
 11.5.52: In Exercises 5154, find the polar equation of the conic with the gi...
 11.5.53: In Exercises 5154, find the polar equation of the conic with the gi...
 11.5.54: In Exercises 5154, find the polar equation of the conic with the gi...
 11.5.55: In Exercises 5558, identify the type of conic, the eccentricity, an...
 11.5.56: In Exercises 5558, identify the type of conic, the eccentricity, an...
 11.5.57: In Exercises 5558, identify the type of conic, the eccentricity, an...
 11.5.58: In Exercises 5558, identify the type of conic, the eccentricity, an...
 11.5.59: Find a polar equation for the hyperbola with focus at the origin, d...
 11.5.60: Let C be the ellipse r = de/(1 + e cos ), where e < 1. Show that th...
 11.5.61: Find an equation in rectangular coordinates of the conic r = 16 5 +...
 11.5.62: Let e > 1. Show that the vertices of the hyperbola r = de 1 + e cos...
 11.5.63: Keplers First Law states that planetary orbits are ellipses with th...
 11.5.64: Keplers Third Law states that the ratio T /a3/2 is equal to a const...
 11.5.65: Verify Theorem 2.
 11.5.66: Verify Theorem 5 in the case 0
 11.5.67: Verify that if e > 1, then Eq. (11) defines a hyperbola of eccentri...
 11.5.68: Reflective Property of the Ellipse In Exercises 6870, we prove that...
 11.5.69: Points R1 and R2 in Figure 25 are defined so that F1R1 and F2R2 are...
 11.5.70: (a) Prove that P F1 = a + x0e and P F2 = a x0e. Hint: Show that P F...
 11.5.71: Here is another proof of the Reflective Property. (a) Figure 25 sug...
 11.5.72: Show that the length QR in Figure 26 is independent of the point P....
 11.5.73: Show that y = x2/4c is the equation of a parabola with directrix y ...
 11.5.74: Consider two ellipses in standard position: E1 : x a1 2 + y b1 2 = ...
 11.5.75: Derive Equations (13) and (14) in the text as follows.Write the coo...
 11.5.76: If we rewrite the general equation of degree 2 (Eq. 12) in terms of...
Solutions for Chapter 11.5: Conic Sections
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 11.5: Conic Sections
Get Full SolutionsChapter 11.5: Conic Sections includes 76 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. Since 76 problems in chapter 11.5: Conic Sections have been answered, more than 40489 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: Calculus: Early Transcendentals , edition: 3.

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

Constant function (on an interval)
ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)

Constant of variation
See Power function.

Coordinate plane
See Cartesian coordinate system.

Definite integral
The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

Domain of a function
The set of all input values for a function

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

Extraneous solution
Any solution of the resulting equation that is not a solution of the original equation.

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.

Graph of parametric equations
The set of all points in the coordinate plane corresponding to the ordered pairs determined by the parametric equations.

Identity
An equation that is always true throughout its domain.

LRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the lefthand endpoint of each subinterval

Pascal’s triangle
A number pattern in which row n (beginning with n = 02) consists of the coefficients of the expanded form of (a+b)n.

Polar axis
See Polar coordinate system.

Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

Probability function
A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.

Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.

Work
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.