The graph is a hyperbola with foci, vertices, and asymptotes. The points on the y-axis are: (0,3) and (0, -3). The points on the x-axis (left to right) are: (-√34,0), (-5,0), (5,0), (√34,0). Choose the correct coordinates of the vertices below. OA. (0,3) and (0, -3) OB. (-5,0) and (5,0) OC. (0,0).(-5,0) and (5,0) Choose the correct coordinates of the foci below. A. (-√34,0) and (√34,0) O B. (0,3) and (0, -3) O C. (-5,0) and (5,0) The equations of the asymptotes are as follows. y = (Simplify your answer. Type an integer or a fraction.) ←

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Hyperbola Graph with Foci, Vertices, and Asymptotes**

- **Points on the y-axis**: (0, 3) and (0, -3).
- **Points on the x-axis** (left to right): \((- \sqrt{34}, 0)\), (-5, 0), (5, 0), \(( \sqrt{34}, 0)\).

**Choose the correct coordinates of the vertices below**:
- A. (0, 3) and (0, -3)
- B. \((-5, 0)\) and (5, 0) **(Correct)**
- C. (0, 0), \((-5, 0)\) and (5, 0)

**Choose the correct coordinates of the foci below**:
- A. \((- \sqrt{34}, 0)\) and \( ( \sqrt{34}, 0) \) **(Correct)**
- B. (0, 3) and (0, -3)
- C. \((-5, 0)\) and (5, 0)

**The equations of the asymptotes are as follows**:

\[ y = \pm \frac{3}{5} x \]

(Simplify your answer. Type an integer or a fraction.)

**Graph Explanation**:
- The image displays a hyperbola centered at the origin (0,0) on a coordinate grid.
- The hyperbola opens horizontally, with vertices marked in red at (-5, 0) and (5, 0).
- The foci marked in green are positioned at approximately \((- \sqrt{34}, 0)\) and \( (\sqrt{34}, 0)\).
- Asymptotes are shown as dashed blue lines, intersecting the origin with slopes of \(\pm \frac{3}{5}\).
- The grid illustrates the classic x and y axes, allowing for easy reference of the coordinates provided.
Transcribed Image Text:**Hyperbola Graph with Foci, Vertices, and Asymptotes** - **Points on the y-axis**: (0, 3) and (0, -3). - **Points on the x-axis** (left to right): \((- \sqrt{34}, 0)\), (-5, 0), (5, 0), \(( \sqrt{34}, 0)\). **Choose the correct coordinates of the vertices below**: - A. (0, 3) and (0, -3) - B. \((-5, 0)\) and (5, 0) **(Correct)** - C. (0, 0), \((-5, 0)\) and (5, 0) **Choose the correct coordinates of the foci below**: - A. \((- \sqrt{34}, 0)\) and \( ( \sqrt{34}, 0) \) **(Correct)** - B. (0, 3) and (0, -3) - C. \((-5, 0)\) and (5, 0) **The equations of the asymptotes are as follows**: \[ y = \pm \frac{3}{5} x \] (Simplify your answer. Type an integer or a fraction.) **Graph Explanation**: - The image displays a hyperbola centered at the origin (0,0) on a coordinate grid. - The hyperbola opens horizontally, with vertices marked in red at (-5, 0) and (5, 0). - The foci marked in green are positioned at approximately \((- \sqrt{34}, 0)\) and \( (\sqrt{34}, 0)\). - Asymptotes are shown as dashed blue lines, intersecting the origin with slopes of \(\pm \frac{3}{5}\). - The grid illustrates the classic x and y axes, allowing for easy reference of the coordinates provided.
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