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2. Let P = 5 5 (1-√) and Q-(1-√√) = 2' 2' 12 12 (a) Compute the hyperbolic distances d(O, P), d(O,Q) and d(P,Q), where O is the origin. (b) Compute the angle

2. Let P = 5 5 (1-√) and Q-(1-√√) = 2' 2' 12 12 (a) Compute the hyperbolic distances d(O, P), d(O,Q) and d(P,Q), where O is the origin. (b) Compute the angle

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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2. Let P = 5 5 (1-√) and Q-(1-√√) = 2' 2' 12 12 (a) Compute the hyperbolic distances d(O, P), d(O,Q) and d(P,Q), where O is the origin. (b) Compute the angle <POQ. (c) Show that the hyperbolic line l = PQ has equation x² 10 3 −x + y² + 1 = 0 (d) Calculate dy and hence show that a tangent vector to l at P is √√15i +7j. Use this to dx compute OPQ.
Transcribed Image Text:2. Let P = 5 5 (1-√) and Q-(1-√√) = 2' 2' 12 12 (a) Compute the hyperbolic distances d(O, P), d(O,Q) and d(P,Q), where O is the origin. (b) Compute the angle <POQ. (c) Show that the hyperbolic line l = PQ has equation x² 10 3 −x + y² + 1 = 0 (d) Calculate dy and hence show that a tangent vector to l at P is √√15i +7j. Use this to dx compute OPQ.
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