Graphing Shifted Hyperbolas An equation of a hyperbola is given. (a) Find the center, vertices, foci, and asymptotes of the hyperbola. (b) Sketch a graph showing the hyperbola and its asymptotes.
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Chapter 11 Solutions
Precalculus: Mathematics for Calculus
- 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?arrow_forwardFill in the blanks. The line segment connecting the vertices of a hyperbola is the , and its midpoint is the of the hyperbola.arrow_forwardProperty of a Hyperbola Use the figure to show that d2d1=2a.arrow_forward
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- Navigation In the figure on the next page, the LORAN stations at A and B are 500 mi apart, and the ship at P receives station A’s signal 2640 microseconds (s) before it receives the signal from station B. Assuming that radio signals travel at 980ft/s , find d(P,A)d(P,B) . Find an equation for the branch of the hyperbola indicated in red in the figure. (Use miles as the unit of distance.) If A is due north of B and if P is due east of A, how far is P from A?arrow_forwardRoad Design Roads are often designed with parabolic surfaces to allow rain to drain off. A particular road is 32 feet wide and 0.4 foot higher in the center than it is on the sides (see figure). (a) Write an equation of the parabola with its vertex at the origin that models the road surface. (b) How far from the center of the road is the road surface 0.1 foot lower than the center?arrow_forward
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