Write the standard form equation for a hyperbola with center at the origin, vertices at (0, 3) and (0, -3), and foci at (0, 6) and (0, -6). It may take a moment for applet to load... 10 Standard Equation of a Vertical Hyperbola Horizontal Axiş 9 Show Traverse Axis y? /9 - x2/ 3.42 = 1 V Vertical Axis 8 Show Center 7 Show Vertices 6 Show co-vertices 5 4 Show Foci Show Asymptotes 2 Eccentricity 1 -14 -13 -12 -11 -10 -9 -8 -7 -6 -4 -1 1 2 3 4 6. 10 11 12 13 -1 Show Directrix -2 Show Point h = 0 -4 Show Latis Rectum -5 a = 3 -6 b=1.85 -8 - -9 -10 -11 -12 -13
Write the standard form equation for a hyperbola with center at the origin, vertices at (0, 3) and (0, -3), and foci at (0, 6) and (0, -6). It may take a moment for applet to load... 10 Standard Equation of a Vertical Hyperbola Horizontal Axiş 9 Show Traverse Axis y? /9 - x2/ 3.42 = 1 V Vertical Axis 8 Show Center 7 Show Vertices 6 Show co-vertices 5 4 Show Foci Show Asymptotes 2 Eccentricity 1 -14 -13 -12 -11 -10 -9 -8 -7 -6 -4 -1 1 2 3 4 6. 10 11 12 13 -1 Show Directrix -2 Show Point h = 0 -4 Show Latis Rectum -5 a = 3 -6 b=1.85 -8 - -9 -10 -11 -12 -13
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
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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![### Understanding the Standard Form of a Hyperbola
To find the standard form equation for a hyperbola with its center at the origin, vertices at (0, 3) and (0, -3), and foci at (0, 6) and (0, -6), follow these steps:
**Graph Explanation:**
- The graph displays a vertical hyperbola centered at the origin.
- **Equation:** The standard form of the vertical hyperbola is given by:
\[
\frac{y^2}{9} - \frac{x^2}{3.42} = 1
\]
**Features Explained:**
- **Center:** The origin (0, 0).
- **Vertices:** Located at (0, 3) and (0, -3).
- **Foci:** Positioned at (0, 6) and (0, -6).
- **Axes Checkboxes:** Options to display Horizontal and Vertical Axes are provided.
- **Additional Options:** You can enable features to show elements like Traverse Axis, Center, Vertices, Co-vertices, Foci, Asymptotes, Eccentricity, Directrix, Point, and Latus Rectum.
**Parameters:**
- \(h = 0\), \(k = 0\) (coordinates of the center)
- \(a = 3\) (distance from the center to each vertex along the y-axis)
- \(b = 1.85\) (related to distance along the x-axis)
These values help in constructing and understanding the geometry and algebra of the hyperbola.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa40ccb8f-82e3-49d1-b352-e9f5be0dea10%2Fe46b7bb5-32a9-4099-93db-95cf027bd35b%2F7agvr6o_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding the Standard Form of a Hyperbola
To find the standard form equation for a hyperbola with its center at the origin, vertices at (0, 3) and (0, -3), and foci at (0, 6) and (0, -6), follow these steps:
**Graph Explanation:**
- The graph displays a vertical hyperbola centered at the origin.
- **Equation:** The standard form of the vertical hyperbola is given by:
\[
\frac{y^2}{9} - \frac{x^2}{3.42} = 1
\]
**Features Explained:**
- **Center:** The origin (0, 0).
- **Vertices:** Located at (0, 3) and (0, -3).
- **Foci:** Positioned at (0, 6) and (0, -6).
- **Axes Checkboxes:** Options to display Horizontal and Vertical Axes are provided.
- **Additional Options:** You can enable features to show elements like Traverse Axis, Center, Vertices, Co-vertices, Foci, Asymptotes, Eccentricity, Directrix, Point, and Latus Rectum.
**Parameters:**
- \(h = 0\), \(k = 0\) (coordinates of the center)
- \(a = 3\) (distance from the center to each vertex along the y-axis)
- \(b = 1.85\) (related to distance along the x-axis)
These values help in constructing and understanding the geometry and algebra of the hyperbola.
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