Problem 1E: Conic Sections State the definitions of parabola, ellipse, and hyperbola in your own words. Problem 2E: Reflective Property Use a sketch to illustrate the reflective property of an ellipse. Problem 3E: Eccentricity Consider an ellipse with eccentricity e. (a) What are the possible values of e. (b)... Problem 4E: Hyperbola Explain how to sketch a hyperbola with a vertical transverse axis. Problem 5E: Matching In Exercises 5-10, match the equation with its graph. [The graphs are labeled (a), (b),... Problem 6E: Matching In Exercises 5-10, match the equation with its graph. [The graphs are labeled (a), (b),... Problem 7E: Matching In Exercises 5-10, match the equation with its graph. [The graphs are labeled (a), (b),... Problem 8E: Matching In Exercises 5-10, match the equation with its graph. [The graphs are labeled (a), (b),... Problem 9E: Matching In Exercises 5-10, match the equation with its graph. [The graphs are labeled (a), (b),... Problem 10E: Matching In Exercises 5-10, match the equation with its graph. [The graphs are labeled (a), (b),... Problem 11E: Sketching a Parabola In Exercises 1116, find the vertex, focus, and directrix of the parabola, and... Problem 12E: Sketching a Parabola In Exercises 1116, find the vertex, focus, and directrix of the parabola, and... Problem 13E: Sketching a Parabola In Exercises 1116, find the vertex, focus, and directrix of the parabola, and... Problem 14E: Sketching a Parabola In Exercises 1116, find the vertex, focus, and directrix of the parabola, and... Problem 15E: Sketching a Parabola In Exercises 1116, find the vertex, focus, and directrix of the parabola, and... Problem 16E: Sketching a Parabola In Exercises 1116, find the vertex, focus, and directrix of the parabola, and... Problem 17E: Finding the Standard Equation of a Parabola In Exercises 17-24, find the standard form of the... Problem 18E: Finding the Standard Equation of a Parabola In Exercises 17-24, find the standard form of the... Problem 19E: Finding the Standard Equation of a Parabola In Exercises 17-24, find the standard form of the... Problem 20E: Find the standard form of the equation of parabola with the given characteristics... Problem 21E: Finding the Standard Equation of a Parabola In Exercises 17-24, find the standard form of the... Problem 22E: Finding the Standard Equation of a Parabola In Exercises 17-24, find the standard form of the... Problem 23E: Finding the Standard Equation of a Parabola In Exercises 1724, find the standard form of the... Problem 24E: Finding the Standard Equation of a Parabola In Exercises 17-24, find the standard form of the... Problem 25E: Sketching an Ellipse In Exercises 2530, find the center, foci, vertices, and eccentricity of the... Problem 26E: Sketching an Ellipse In Exercises 2530, find the center, foci, vertices, and eccentricity of the... Problem 27E: Sketching an Ellipse In Exercises 2530, find the center, foci, vertices, and eccentricity of the... Problem 28E: Sketching an Ellipse In Exercises 2530, find the center, foci, vertices, and eccentricity of the... Problem 29E Problem 30E: Sketching an Ellipse In Exercises 2530, find the center, foci, vertices, and eccentricity of the... Problem 31E: Finding the Standard Equation of an Ellipse In Exercises 31-36, find the standard form of the... Problem 32E Problem 33E Problem 34E: Finding the Standard Equation of an Ellipse In Exercises 31-36, find the standard form of the... Problem 35E: Finding the Standard Equation of an Ellipse In Exercises 3136, find the standard form of the... Problem 36E: Finding the Standard Equation of an Ellipse In Exercises 3136, find the standard form of the... Problem 37E: Sketching a Hyperbola In Exercises 37-40, find the center, foci, vertices, and eccentricity of the... Problem 38E: Sketching a Hyperbola In Exercises 37-40, find the center, foci, vertices, and eccentricity of the... Problem 39E: Sketching a Hyperbola In Exercises 37-40, find the center, foci, vertices, and eccentricity of the... Problem 40E Problem 41E: Finding the Standard Equation of a Hyperbola In Exercises 4148, find the standard form of the... Problem 42E: Finding the Standard Equation of a Hyperbola In Exercises 4148, find the standard form of the... Problem 43E: Finding the Standard Equation of a Hyperbola In Exercises 4148, find the standard form of the... Problem 44E Problem 45E: Finding the Standard Equation of a Hyperbola In Exercises 41-48, find the standard form of the... Problem 46E: Finding the Standard Equation of a Hyperbola In Exercises 4148, find the standard form of the... Problem 47E: Finding the Standard Equation of a Hyperbola In Exercises 41-48, find the standard form of the... Problem 48E: Finding the Standard Equation of a Hyperbola In Exercises 4148, find the standard form of the... Problem 49E: Finding Equations of Tangent Lines and Normal Lines In Exercises 49 and 50, find equations fur (a)... Problem 50E Problem 51E: Classifying the Graph of an Equation In Exercises 51-56, classify the graph of the equation as a... Problem 52E Problem 53E Problem 54E Problem 55E: Classifying the Graph of an Equation In Exercises 51-56, classify the graph of the equation as a... Problem 56E Problem 57E Problem 58E Problem 59E Problem 60E: HOW DO YOU SEE IT? Describe in words bow a plane could intersect with the double-napped cone to form... Problem 61E: Solar Collector A solar collector for heating water is constructed with a sheet of stainless steel... Problem 62E: Beam Deflection A simply supported beam that is 16 meters long has a load concentrated at the center... Problem 63E: Proof (a) Prove that any two distinct tangent lines to a parabola interact. (b) Demonstrate the... Problem 64E Problem 65E: Bridge Design A cable of a suspension bridge is suspended (in the shape of a parabola) between two... Problem 66E Problem 67E Problem 68E: Surface Area A satellite signal receiving dish is formed by revolving the parabola given by x2=20y... Problem 69E: Orbit of Earth Earth moves in an elliptical orbit with the sun at one of the foci. The length of... Problem 70E: Satellite Orbit The apogee(the point in orbit farthest from Earth) and the perigee (the point in... Problem 71E Problem 72E Problem 73E: Halleys Comet Probably the most famous of all comets, Halleys comet, has an elliptical orbit with... Problem 74E Problem 75E Problem 76E Problem 77E: Arc Length Use the integration capabilities of a graphing utility to approximate to... Problem 78E Problem 79E: Geometry The area of the ellipse in the figure is twice the area of the circle. What is the length... Problem 80E: Proof Prove Theorem 10.4 by showing dial the tangent line to an ellipse at a point P makes equal... Problem 81E Problem 82E: Hyperbola Consider a hyperbola centered at the origin with a horizontal transverse axis. Use the... Problem 83E: Navigation LORAN (long distance radio navigation) for aircraft and ships uses synchronized pulses... Problem 84E: Hyperbolic Mirror A hyperbolic mirror (used in some telescopes) has the property that a light ray... Problem 85E Problem 86E: Proof Prove that the graph of the equation Ax2+Cy2+Dx+Ey+F=0 is one of the following (except in... Problem 87E Problem 88E Problem 89E Problem 90E: True or False? In Exercises 87-92, determine whether the statement is true or false. If it is false,... Problem 91E: True or False? In Exercises 8792, determine whether the statement is true or false. If it is false,... Problem 92E Problem 93E: For a point P on an ellipse, let d be the distance from the center of the ellipse to the line... Problem 94E: Find the minimum value of (uv)2+(2u29v)2 for 0u2 and v0. format_list_bulleted