 10.4.1: Identify the conic.(a) The set of points in the plane, the sum of w...
 10.4.2: (a) The equation of the parabola with focus (p, 0) and directrixx =...
 10.4.3: (a) Suppose that an ellipse has semimajor axis a andsemiminor axis ...
 10.4.4: (a) Suppose that a hyperbola has semifocal axis a and semiconjugate...
 10.4.5: 36 Sketch the parabola, and label the focus, vertex, and directrix....
 10.4.6: 36 Sketch the parabola, and label the focus, vertex, and directrix....
 10.4.7: 710 Sketch the ellipse, and label the foci, vertices, and endsof th...
 10.4.8: 710 Sketch the ellipse, and label the foci, vertices, and endsof th...
 10.4.9: 710 Sketch the ellipse, and label the foci, vertices, and endsof th...
 10.4.10: 710 Sketch the ellipse, and label the foci, vertices, and endsof th...
 10.4.11: 1114 Sketch the hyperbola, and label the vertices, foci, andasympto...
 10.4.12: 1114 Sketch the hyperbola, and label the vertices, foci, andasympto...
 10.4.13: 1114 Sketch the hyperbola, and label the vertices, foci, andasympto...
 10.4.14: 1114 Sketch the hyperbola, and label the vertices, foci, andasympto...
 10.4.15: 1518 Find an equation for the parabola that satisfies the givencond...
 10.4.16: 1518 Find an equation for the parabola that satisfies the givencond...
 10.4.17: 1518 Find an equation for the parabola that satisfies the givencond...
 10.4.18: 1518 Find an equation for the parabola that satisfies the givencond...
 10.4.19: 1922 Find an equation for the ellipse that satisfies the givencondi...
 10.4.20: 1922 Find an equation for the ellipse that satisfies the givencondi...
 10.4.21: 1922 Find an equation for the ellipse that satisfies the givencondi...
 10.4.22: 1922 Find an equation for the ellipse that satisfies the givencondi...
 10.4.23: 2326 Find an equation for a hyperbola that satisfies the givencondi...
 10.4.24: 2326 Find an equation for a hyperbola that satisfies the givencondi...
 10.4.25: 2326 Find an equation for a hyperbola that satisfies the givencondi...
 10.4.26: 2326 Find an equation for a hyperbola that satisfies the givencondi...
 10.4.27: 2730 TrueFalse Determine whether the statement is true orfalse. Exp...
 10.4.28: 2730 TrueFalse Determine whether the statement is true orfalse. Exp...
 10.4.29: 2730 TrueFalse Determine whether the statement is true orfalse. Exp...
 10.4.30: 2730 TrueFalse Determine whether the statement is true orfalse. Exp...
 10.4.31: (a) As illustrated in the accompanying figure, a parabolicarch span...
 10.4.32: (a) Find an equation for the parabolic arch with base b andheight h...
 10.4.33: Show that the vertex is the closest point on a parabola tothe focus...
 10.4.34: As illustrated in the accompanying figure, suppose that acomet move...
 10.4.35: For the parabolic reflector in the accompanying figure, howfar from...
 10.4.36: (a) Show that the right and left branches of the hyperbolax2a2 y2b2...
 10.4.37: (a) Show that the right and left branches of the hyperbolax2a2 y2b2...
 10.4.38: Find an equation of the parabola traced by a point that movesso tha...
 10.4.39: Find an equation of the ellipse traced by a point that movesso that...
 10.4.40: Find the equation of the hyperbola traced by a point thatmoves so t...
 10.4.41: Suppose that the base of a solid is elliptical with a major axisof ...
 10.4.42: Suppose that the base of a solid is elliptical with a major axisof ...
 10.4.43: Show that an ellipse with semimajor axis a and semiminoraxis b has ...
 10.4.44: Show that if a plane is not parallel to the axis of a rightcircular...
 10.4.45: As illustrated in the accompanying figure on the nextpage, a carpen...
 10.4.46: As illustrated in the accompanying figure, suppose thattwo observer...
 10.4.47: As illustrated in the accompanying figure, suppose thattwo transmit...
 10.4.48: A nuclear cooling tower is to have a height of h feet andthe shape ...
 10.4.49: Let R be the region that is above the xaxis and enclosedbetween th...
 10.4.50: As illustrated in the accompanying figure, the tank ofan oil truck ...
 10.4.51: . Prove: The line tangent to the parabola x2 = 4py at thepoint (x0,...
 10.4.52: Prove: The line tangent to the ellipsex2a2 + y2b2 = 1at the point (...
 10.4.53: Prove: The line tangent to the hyperbolax2a2 y2b2 = 1at the point (...
 10.4.54: Use the results in Exercises 52 and 53 to show that if an ellipsean...
 10.4.55: Find two values of k such that the line x + 2y = k is tangentto the...
 10.4.56: Find the coordinates of all points on the hyperbola4x2 y2 = 4where ...
 10.4.57: A line tangent to the hyperbola 4x2 y2 = 36 intersects theyaxis at...
 10.4.58: Consider the seconddegree equationAx2 + Cy2 + Dx + Ey + F = 0where...
 10.4.59: In each part, use the result in Exercise 58 to make a statementabou...
 10.4.60: Derive the equation x2 = 4py in Figure 10.4.6.
 10.4.61: Derive the equation (x2/b2) + (y2/a2) = 1 given in Figure 10.4.14.
 10.4.62: Derive the equation (x2/a2) (y2/b2) = 1 given in Figure 10.4.22.
 10.4.63: Prove Theorem 10.4.4. [Hint: Choose coordinate axes sothat the para...
 10.4.64: Given two intersecting lines, letL2 be the line with the largerangl...
 10.4.65: Writing Suppose that you want to draw an ellipse that hasgiven valu...
 10.4.66: Writing List the forms for standard equations of parabolas,ellipses...
Solutions for Chapter 10.4: CONIC SECTIONS
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 10.4: CONIC SECTIONS
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. Since 66 problems in chapter 10.4: CONIC SECTIONS have been answered, more than 41900 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. Chapter 10.4: CONIC SECTIONS includes 66 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Acute triangle
A triangle in which all angles measure less than 90°

Algebraic expression
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots

Arcsine function
See Inverse sine function.

Causation
A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable

Cycloid
The graph of the parametric equations

Directed distance
See Polar coordinates.

DMS measure
The measure of an angle in degrees, minutes, and seconds

Double inequality
A statement that describes a bounded interval, such as 3 ? x < 5

Grapher or graphing utility
Graphing calculator or a computer with graphing software.

Infinite limit
A special case of a limit that does not exist.

Linear programming problem
A method of solving certain problems involving maximizing or minimizing a function of two variables (called an objective function) subject to restrictions (called constraints)

Minor axis
The perpendicular bisector of the major axis of an ellipse with endpoints on the ellipse.

Quotient of functions
a ƒ g b(x) = ƒ(x) g(x) , g(x) ? 0

Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

Solve by substitution
Method for solving systems of linear equations.

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Symmetric about the yaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Terminal side of an angle
See Angle.

Vertex of an angle
See Angle.

xyplane
The points x, y, 0 in Cartesian space.