Title: Ellipse part three
Course: 2025 Probabilidad y Estadística

Q: Find the center of the ellipse.

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[Image]
- (8, 2) (Correct)
- (5, 4) (Incorrect)
- (0, 0) (Incorrect)
- (4, 5) (Incorrect)
- (2, 8) (Incorrect)
A: (8, 2)

Q: Find the foci and vertices of the ellipse.

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[Image]
- vertices (14, -9), (4,-9); foci [Image] (Correct)
- vertices (0, 0); foci [Image] (Incorrect)
- vertices (5, 8), (-5, -8); foci (9, -9), (9, 9) (Incorrect)
- vertices [Image]; foci (14, 9), (4, 9) (Incorrect)
- none of these (Incorrect)
A: vertices (14, -9), (4,-9); foci [Image]

Q: Find the center, foci, and vertices of the ellipse, and determine the lengths of the major and minor axes. Then sketch the graph.

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​ [Image]
- The length of the major axis is 10, and the length of the minor axis is 6 [Image] ​ (Correct)
- The length of the major axis is 11, and the length of the minor axis is 6 [Image] ​ (Incorrect)
- The length of the major axis is 10, and the length of the minor axis is 6 [Image] ​ (Incorrect)
- The length of the major axis is 10, and the length of the minor axis is 6 [Image] ​ (Incorrect)
- The length of the major axis is 10, and the length of the minor axis is 6 [Image] ​ (Incorrect)
A: The length of the major axis is 10, and the length of the minor axis is 6 [Image] ​

Q: Find the center, foci, and vertices of the ellipse, and determine the lengths of the major and minor axes. Then sketch the graph.

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[Image]
- The length of the major axis is 4, and the length of the minor axis is 2 [Image] (Incorrect)
- The length of the major axis is 4, and the length of the minor axis is 2 [Image] (Incorrect)
- The length of the major axis is 4, and the length of the minor axis is 2 [Image] (Correct)
- The length of the major axis is 4, and the length of the minor axis is 2 [Image] (Incorrect)
- The length of the major axis is 4, and the length of the minor axis is 2 [Image] (Incorrect)
A: The length of the major axis is 4, and the length of the minor axis is 2 [Image]

Q: Given the equation of the ellipse in the standard form \( \frac{(x-2)^2}{9}+ \frac{(y+5)^2}{25}=1 \) determine the value of a.
A: 5

Q: Given the equation of the ellipse in the standard form \( \frac{(x-2)^2}{9}+ \frac{(y+5)^2}{25}=1 \) determine the value of b.
A: 3

Q: Given the equation of the ellipse in the standard form \( \frac{(x-2)^2}{9}+ \frac{(y+5)^2}{25}=1 \) determine the value of c.
A: 4

Q: Given the equation of the ellipse in the standard form \( \frac{(x-2)^2}{9}+ \frac{(y+5)^2}{25}=1 \) determine the length of focal axis.
A: 8

Q: Given the equation of the ellipse in the standard form \( \frac{(x-2)^2}{9}+ \frac{(y+5)^2}{25}=1 \) determine the length of latus rectum.  Input your answer in decimal form.
A: 3.6

Q: Given the equation of the ellipse in the standard form \( \frac{(x-2)^2}{9}+ \frac{(y+5)^2}{25}=1 \) determine the eccentricity. Input your answer in decimal form.
A: 0.8