An equation of an ellipse is given. x² + y² 25 1 16 (a) Find the vertices, foci, and eccentricity of the ellipse. vertex (x, y) = (smaller x-value) vertex (х, у) - (larger x-value) focus (x, y) = (smaller x-value) focus (х, у) %3D (larger x-value) eccentricity (b) Determine the length of the major axis. Determine the length of the minor axis. (c) Sketch a graph of the ellipse.
An equation of an ellipse is given. x² + y² 25 1 16 (a) Find the vertices, foci, and eccentricity of the ellipse. vertex (x, y) = (smaller x-value) vertex (х, у) - (larger x-value) focus (x, y) = (smaller x-value) focus (х, у) %3D (larger x-value) eccentricity (b) Determine the length of the major axis. Determine the length of the minor axis. (c) Sketch a graph of the ellipse.
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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![### An equation of an ellipse is given.
\[
\frac{x^2}{25} + \frac{y^2}{16} = 1
\]
#### (a) Find the vertices, foci, and eccentricity of the ellipse.
- **Vertex**
- \((x, y) = \Bigg( \underline{\hspace{1cm}} , \underline{\hspace{1cm}} \Bigg)\) (smaller x-value)
- \((x, y) = \Bigg( \underline{\hspace{1cm}} , \underline{\hspace{1cm}} \Bigg)\) (larger x-value)
- **Focus**
- \((x, y) = \Bigg( \underline{\hspace{1cm}} , \underline{\hspace{1cm}} \Bigg)\) (smaller x-value)
- \((x, y) = \Bigg( \underline{\hspace{1cm}} , \underline{\hspace{1cm}} \Bigg)\) (larger x-value)
- **Eccentricity**
- \(\underline{\hspace{2cm}}\)
#### (b) Determine the length of the major axis.
- \(\underline{\hspace{5cm}}\)
#### Determine the length of the minor axis.
- \(\underline{\hspace{5cm}}\)
#### (c) Sketch a graph of the ellipse.
- *Explain or draw the graph of the ellipse based on the given equation.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab2998ba-0f3d-4786-bf36-9b4f07bdc270%2F23ca997f-4768-4727-bb09-738fe1323ed0%2F12fkap_processed.png&w=3840&q=75)
Transcribed Image Text:### An equation of an ellipse is given.
\[
\frac{x^2}{25} + \frac{y^2}{16} = 1
\]
#### (a) Find the vertices, foci, and eccentricity of the ellipse.
- **Vertex**
- \((x, y) = \Bigg( \underline{\hspace{1cm}} , \underline{\hspace{1cm}} \Bigg)\) (smaller x-value)
- \((x, y) = \Bigg( \underline{\hspace{1cm}} , \underline{\hspace{1cm}} \Bigg)\) (larger x-value)
- **Focus**
- \((x, y) = \Bigg( \underline{\hspace{1cm}} , \underline{\hspace{1cm}} \Bigg)\) (smaller x-value)
- \((x, y) = \Bigg( \underline{\hspace{1cm}} , \underline{\hspace{1cm}} \Bigg)\) (larger x-value)
- **Eccentricity**
- \(\underline{\hspace{2cm}}\)
#### (b) Determine the length of the major axis.
- \(\underline{\hspace{5cm}}\)
#### Determine the length of the minor axis.
- \(\underline{\hspace{5cm}}\)
#### (c) Sketch a graph of the ellipse.
- *Explain or draw the graph of the ellipse based on the given equation.*
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