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2. Let l be the line x² + y² − 4x + 2y +1 = 0 and drop a perpendicular from O to Q E l. (a) Explain why Q has co-ordinates (✓t, - ✓t) for some t = (0,1). (b) Show that the hyperbolic distance 8 = d(O,Q) of l from the origin is In 1+15. 2 (c) = (0,-1) is an omega-point for l. Compute the angle of parallelism μ = LQON Ω explicitly and check that cosh 8 = cscµ.

2. Let l be the line x² + y² − 4x + 2y +1 = 0 and drop a perpendicular from O to Q E l. (a) Explain why Q has co-ordinates (✓t, - ✓t) for some t = (0,1). (b) Show that the hyperbolic distance 8 = d(O,Q) of l from the origin is In 1+15. 2 (c) = (0,-1) is an omega-point for l. Compute the angle of parallelism μ = LQON Ω explicitly and check that cosh 8 = cscµ.

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 l be the line x² + y² − 4x + 2y +1 = 0 and drop a perpendicular from O to Q E l. (a) Explain why Q has co-ordinates (✓t, - ✓t) for some t = (0,1). (b) Show that the hyperbolic distance 8 = d(O,Q) of l from the origin is In 1+15. 2 (c) = (0,-1) is an omega-point for l. Compute the angle of parallelism μ = LQON Ω explicitly and check that cosh 8 = cscµ.
Transcribed Image Text:2. Let l be the line x² + y² − 4x + 2y +1 = 0 and drop a perpendicular from O to Q E l. (a) Explain why Q has co-ordinates (✓t, - ✓t) for some t = (0,1). (b) Show that the hyperbolic distance 8 = d(O,Q) of l from the origin is In 1+15. 2 (c) = (0,-1) is an omega-point for l. Compute the angle of parallelism μ = LQON Ω explicitly and check that cosh 8 = cscµ.
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