In Exercises 11-18, find the standard form of the equation of the ellipse with the given characteristics and center at the origin. 11. 12. (0.) (0, 4) (2, 0) (-2, 0) (-2, 0) (2. 0) -8 -4 4 (0.-4) enri 2

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Could you answer questions 11, 13, 15, 19, 21, 23, 25, 27, 29, 35, 39, 41

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## Chapter 10: Topics in Analytic Geometry

### Section 10.3

## EXERCISES

### VOCABULARY: Fill in the blanks.
1. An __________ is the set of all points (x, y) in a plane, the sum of whose distances from two distinct fixed points, called __________, is constant.
2. The chord joining the vertices of an ellipse is called the __________, and its midpoint is the __________ of the ellipse.
3. The chord perpendicular to the major axis at the center of the ellipse is called the __________ of the ellipse.
4. The concept of __________ is used to measure the ovalness of an ellipse.

### SKILLS AND APPLICATIONS
In Exercises 5–10, match the equation with its graph. The graphs are labeled (a), (b), (c), (d), (e), and (f).

**Graphs:**
- (a) A horizontal ellipse centered at the origin.
- (b) A vertical ellipse centered at the y-axis.
- (c) An ellipse centered at point (0,3) with horizontal major axis.
- (d) An ellipse centered at point (2, 0) with vertical major axis.
- (e) An ellipse centered at the origin with a tilted major axis.
- (f) An ellipse centered at (0, -3) with vertical major axis.

**Equations:**
5. \(\frac{x^2}{9} + \frac{y^2}{16} = 1\)
6. \(\frac{x^2}{16} + \frac{y^2}{9} = 1\)
7. \(\frac{(x + 2)^2}{9} + \frac{y^2}{16} = 1\)
8. \(\frac{(x - 2)^2}{4} + \frac{(y + 1)^2}{1} = 1\)
9. \(\frac{x^2}{9} + \frac{(y - 3)^2}{4} = 1\)
10. \(\frac{(x + 2)^2}{4} + \frac{(y - 2)^2}{9} = 1\)

In Exercises 11–18, find the standard form of the equation of the ellipse with the given characteristics and center at the origin.

**Examples
Transcribed Image Text:## Chapter 10: Topics in Analytic Geometry ### Section 10.3 ## EXERCISES ### VOCABULARY: Fill in the blanks. 1. An __________ is the set of all points (x, y) in a plane, the sum of whose distances from two distinct fixed points, called __________, is constant. 2. The chord joining the vertices of an ellipse is called the __________, and its midpoint is the __________ of the ellipse. 3. The chord perpendicular to the major axis at the center of the ellipse is called the __________ of the ellipse. 4. The concept of __________ is used to measure the ovalness of an ellipse. ### SKILLS AND APPLICATIONS In Exercises 5–10, match the equation with its graph. The graphs are labeled (a), (b), (c), (d), (e), and (f). **Graphs:** - (a) A horizontal ellipse centered at the origin. - (b) A vertical ellipse centered at the y-axis. - (c) An ellipse centered at point (0,3) with horizontal major axis. - (d) An ellipse centered at point (2, 0) with vertical major axis. - (e) An ellipse centered at the origin with a tilted major axis. - (f) An ellipse centered at (0, -3) with vertical major axis. **Equations:** 5. \(\frac{x^2}{9} + \frac{y^2}{16} = 1\) 6. \(\frac{x^2}{16} + \frac{y^2}{9} = 1\) 7. \(\frac{(x + 2)^2}{9} + \frac{y^2}{16} = 1\) 8. \(\frac{(x - 2)^2}{4} + \frac{(y + 1)^2}{1} = 1\) 9. \(\frac{x^2}{9} + \frac{(y - 3)^2}{4} = 1\) 10. \(\frac{(x + 2)^2}{4} + \frac{(y - 2)^2}{9} = 1\) In Exercises 11–18, find the standard form of the equation of the ellipse with the given characteristics and center at the origin. **Examples
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