Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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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.*](https://content.bartleby.com/qna-images/question/ab2998ba-0f3d-4786-bf36-9b4f07bdc270/23ca997f-4768-4727-bb09-738fe1323ed0/12fkap_processed.png)
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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