33-36 - Graphing Hyperbolas Use a graphing device to graphthe hyperbola.-33. x - 2y? – 834. 3y - 4x – 2435.2= 1636.10064

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College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter7: Conic Sections

Section7.3: Hyperbolas

Problem 33E

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Similar questions

Sonic boom The position of a sonic boom caused by the faster-than-sound aircraft is one branch of the hyperbola y2x2=25 in the coordinate system shown. How wide is the hyperbola 5 miles from its vertex?
a Give the geometric definition of a hyperbola. b Give the equation of a hyperbola with the center at the origin and traverse axis along the x axis. How long is the traverse axis? Where are the vertices? What are the asymptotes? What are the asymptotes? Where are the foci? c What is a good first step in graphing the hyperbola that is described in part b ? d Graph the equation x216y29=1. What are the asymptotes? Where are the vertices? Where are the foci? What is the length of the transverse axis?
Property of a Hyperbola Use the figure to show that d2d1=2a.
CONCEPTS A Hyperbola is the set of all points in the plane for which the of the distances from two fixed points F1 and F2 is constant. The point F1 and F2 are called the of the hyperbola.
DISCUSS: Light from a Lamp The light from a lamp forms a lighted area on a wall, as shown in the figure. Why is the boundary of this lighted area a hyperbola? How can one hold a flashlight so that its beam forms a hyperbola on the ground?
Perpendicular Asymptotes Show that the asymptotes of the hyperbola x2y2=5 are perpendicular to each other. Find an equation for the hyperbola with foci (c,0) and with asymptotes perpendicular to each other.
When an airplane travels faster than the speed of sound, the sound waves form a cone behind the airplane. If the airplane is flying parallel to the ground, then the sound waves intersect the ground in a hyperbola with the airplane directly above its center, and a sonic boom is heard along the hyperbola. You hear a sonic boom that is audible along a hyperbola with the equation (x2/100)(y2/4)=1, where x and y are measured in miles. What is the shortesthorizontal distance you could be from the airplane?

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33-36 - Graphing Hyperbolas Use a graphing device to graph the hyperbola. -33. x - 2y? – 8 34. 3y - 4x – 24 35. 2 = 1 6 36. 100 64