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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F833bf7b1-3e6b-4749-8e88-54090320a3f5%2F42d7f900-e222-40d5-b816-5530983b544b%2Fogdoc7g_processed.png&w=3840&q=75)
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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