Finding the Standard Equation of a Hyperbola InExercises 11-20, find the standard form of the equationof the hyperbola with the given characteristics.11. Vertices: (0, ±2); foci: (0, ±4)

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Answered: Finding the Standard Equation of a…

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 37E

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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.
Property of a Hyperbola Use the figure to show that d2d1=2a.
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.
Finding the Equation of a Parabola Find an equation for the parabola that has its vertex at the origin and satisfies the given condition(s). Focus on the positive x-axis, 2 units away from the directrix
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?
Finding the Equation of a Parabola Find an equation for the parabola that has its vertex at the origin and satisfies the given condition(s). Focal diameter 8 and focus on the negative y-axis
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?

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Finding the Standard Equation of a Hyperbola In Exercises 11-20, find the standard form of the equation of the hyperbola with the given characteristics. 11. Vertices: (0, ±2); foci: (0, +4)