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ci at (0, -15), (0, 15) 912) 55-12) (0, 15) 1/² (@01-15) , (2, 2); eccentricity 5/4 X

ci at (0, -15), (0, 15) 912) 55-12) (0, 15) 1/² (@01-15) , (2, 2); eccentricity 5/4 X

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Write an equation for the hyperbola
**Hyperbolas: Key Concepts and Examples** **2) y-intercepts ± 12; foci at (0, -15), (0, 15)** - The graph depicts a hyperbola centered at the origin (0,0) with its transverse axis along the y-axis. - The vertices are at (0,12) and (0,-12). - The foci are at (0,15) and (0,-15). **Handwritten Notes:** - There is a sketch of a coordinate plane with the hyperbola displaying its vertices at (0,12) and (0,-12). - The foci are marked at (0,15) and (0,-15). - An equation format: \(\frac{y^2}{144} - \frac{x^2}{b^2} = 1\) is written, indicating a vertical hyperbola. **3) vertices at (2, 10), (2, 2); eccentricity \(\frac{5}{4}\)** - The vertices are at (2,10) and (2,2), suggesting a vertical orientation of the hyperbola. - The eccentricity is given as \(\frac{5}{4}\), which is a measure of how much the conic section deviates from being circular. **Summary:** This section has focused on the properties and components of hyperbolas, including vertices, foci, and the concept of eccentricity. Understanding these fundamental parts helps in sketching and analyzing hyperbolas based on given conditions.
Transcribed Image Text:**Hyperbolas: Key Concepts and Examples** **2) y-intercepts ± 12; foci at (0, -15), (0, 15)** - The graph depicts a hyperbola centered at the origin (0,0) with its transverse axis along the y-axis. - The vertices are at (0,12) and (0,-12). - The foci are at (0,15) and (0,-15). **Handwritten Notes:** - There is a sketch of a coordinate plane with the hyperbola displaying its vertices at (0,12) and (0,-12). - The foci are marked at (0,15) and (0,-15). - An equation format: \(\frac{y^2}{144} - \frac{x^2}{b^2} = 1\) is written, indicating a vertical hyperbola. **3) vertices at (2, 10), (2, 2); eccentricity \(\frac{5}{4}\)** - The vertices are at (2,10) and (2,2), suggesting a vertical orientation of the hyperbola. - The eccentricity is given as \(\frac{5}{4}\), which is a measure of how much the conic section deviates from being circular. **Summary:** This section has focused on the properties and components of hyperbolas, including vertices, foci, and the concept of eccentricity. Understanding these fundamental parts helps in sketching and analyzing hyperbolas based on given conditions.
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