Title: Hyperbola at (h,k)
Course: 2025 Probabilidad y Estadística

Q: Find the foci and vertices of the hyperbola.

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y^2- 25x^2- 12y- 200x- 389 = 0
- vertices (-9, 6), (-4, -1), foci (-4, 6), (4, 6) (Incorrect)
- vertices (11, 4), (1, 4), foci [Image] (Incorrect)
- vertices [Image], foci (-4, 11), (-4, 1) (Incorrect)
- vertices (-4, 11), (-4, 1), foci [Image] (Correct)
- vertices (4, 11), (4, 1), foci [Image] (Incorrect)
A: vertices (-4, 11), (-4, 1), foci [Image]

Q: Find the center and vertices of the hyperbola.

(x- 7) ^2- (y + 6) ^2 = 1
- center (7, -6), vertices (8, -6), (6, -6) (Correct)
- center (6, -7), vertices (6, 8), (6, 6) (Incorrect)
- center (0, 0), foci (7, -6), (-7, 6) (Incorrect)
- center (0, 0), foci (-7, 6), (7, -6) (Incorrect)
- center (-7, 6), vertices (-8, -6), (-6, 6) (Incorrect)
A: center (7, -6), vertices (8, -6), (6, -6)

Q: Find the center, foci, vertices, and asymptotes of the hyperbola. Then sketch the graph.

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[Image]
- [Image] (Correct)
- [Image] (Incorrect)
- [Image] (Incorrect)
- [Image] (correct)
- [Image] (Incorrect)
A: [Image] / [Image]

Q: Find the foci and asymptotes of the hyperbola.

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[Image]
- asymptotes [Image], foci [Image] (Incorrect)
- asymptotes [Image], foci [Image] (Incorrect)
- asymptotes [Image], foci [Image] (Correct)
- asymptotes [Image], foci [Image] (Incorrect)
- asymptotes [Image], foci [Image] (Incorrect)
A: asymptotes [Image], foci [Image]

Q: Find the center, foci, vertices, and asymptotes of the hyperbola. Then sketch the graph.

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[Image]
- [Image] The center is (3, 1), the foci are [Image], the vertices are (3, 6) and (3, -4), and the asymptotes are [Image] and [Image] (Incorrect)
- [Image] The center is (-3, 1), the foci are [Image], the vertices are (-3, 4) and (-3, -2), and the asymptotes are [Image] and [Image] (Correct)
- [Image] The center is (3, 1), the foci are [Image], the vertices are (9, 1) and (3, 1), and the asymptotes are [Image] and [Image] (Incorrect)
- [Image] The center is (-3, 1), the foci are [Image], the vertices are (-10, 1) and (-4, 1), and the asymptotes are [Image] and [Image] (Incorrect)
- [Image] The center is (-3, 1), the foci are [Image], the vertices are (-7, 1) and (-1, 1), and the asymptotes are [Image] and [Image] (Incorrect)
A: [Image] The center is (-3, 1), the foci are [Image], the vertices are (-3, 4) and (-3, -2), and the asymptotes are [Image] and [Image]

Q: Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic. If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. Then sketch the graph of the equation.

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[Image]
- Parabola [Image] (Correct)
- Hyperbola [Image] (Incorrect)
- Degenerate conic [Image] (Incorrect)
- Ellipse [Image] The length of major axis is 10, and the length of minor axis is 6. (Incorrect)
- The graph is empty. (Incorrect)
A: Parabola [Image]

Q: Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic. If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. Then sketch the graph of the equation.

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[Image]
- Ellipse [Image] The length of major axis is 8, and the length of minor axis is 6. (Correct)
- Parabola [Image] (Incorrect)
- Hyperbola [Image] (Incorrect)
- Degenerate conic [Image] (Incorrect)
- The graph is empty. (Incorrect)
A: Ellipse [Image] The length of major axis is 8, and the length of minor axis is 6.

Q: Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic. If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. Then sketch the graph of the equation.

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[Image]
- Parabola [Image] (Incorrect)
- Degenerate conic [Image] (Incorrect)
- Ellipse [Image] The length of major axis is [Image], and the length of minor axis is 2. (Correct)
- The graph is empty. (Incorrect)
- Hyperbola [Image] (Incorrect)
A: Ellipse [Image] The length of major axis is [Image], and the length of minor axis is 2.

Q: Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic. If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. Then sketch the graph of the equation.

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[Image]
- Degenerate conic [Image] (Incorrect)
- Parabola [Image] (Correct)
- Hyperbola [Image] (Incorrect)
- Ellipse [Image] The length of major axis is [Image], and the length of minor axis is 2. (Incorrect)
- The graph is empty. (Incorrect)
A: Parabola [Image]

Q: Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic. If the graph is an ellipse, find the center, foci, vertices, and lengths of the major and minor axes. If it is a parabola, find the vertex, focus, and directrix. If it is a hyperbola, find the center, foci, vertices, and asymptotes. Then sketch the graph of the equation.

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[Image]
- Degenerate conic [Image] (Incorrect)
- The graph is empty. (Correct)
- Hyperbola [Image] (Incorrect)
- Ellipse [Image] The length of major axis is 10, and the length of minor axis is 6. (Incorrect)
- Parabola [Image] (Incorrect)
A: The graph is empty.