Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
Bartleby Related Questions Icon

Related questions

Q: Find the standard form of the equation of the ellipse satisfying the following conditions. Major…
A: The standard form of the equation of an ellipse with center (h,k) and major axis parallel to the…
Q: 1. minor axis a. the endpoints of the major axis b. the line segment connecting endpoints of the…
A: we have to match the parts with ellipse description.
Q: How do you determine the eccentricity of an ellipse? You can use a figure to express your thoughts…
A: To answer the question that H=how do you determine the eccentricity of an ellipse.
Question
**Problem: Finding the Equation of an Ellipse** To find the equation of the ellipse depicted on the graph, we need to analyze the graph in the image. **Graph Description:** - The graph features a coordinate plane with an ellipse centered at the origin (0, 0). - The x-axis and y-axis both range from -10 to 10. - The ellipse is vertically oriented, meaning it is taller than it is wide. **Ellipse Characteristics:** - The semi-major axis (along the y-direction) extends from -5 to 5 on the y-axis, giving it a length of 10. Therefore, the length of the semi-major axis is 5. - The semi-minor axis (along the x-direction) extends from -2 to 2 on the x-axis, giving it a length of 4. Therefore, the length of the semi-minor axis is 2. **Equation Form:** The equation of an ellipse centered at the origin, with a semi-major axis along the y-axis and a semi-minor axis along the x-axis, is given by: \[ \frac{x^2}{b^2} + \frac{y^2}{a^2} = 1 \] Where: - \(a\) is the semi-major axis length (5). - \(b\) is the semi-minor axis length (2). **Plugging in the Values:** \[ \frac{x^2}{2^2} + \frac{y^2}{5^2} = 1 \] This simplifies to: \[ \frac{x^2}{4} + \frac{y^2}{25} = 1 \] Thus, the equation of the ellipse is: \[ \frac{x^2}{4} + \frac{y^2}{25} = 1 \]
expand button
Transcribed Image Text:**Problem: Finding the Equation of an Ellipse** To find the equation of the ellipse depicted on the graph, we need to analyze the graph in the image. **Graph Description:** - The graph features a coordinate plane with an ellipse centered at the origin (0, 0). - The x-axis and y-axis both range from -10 to 10. - The ellipse is vertically oriented, meaning it is taller than it is wide. **Ellipse Characteristics:** - The semi-major axis (along the y-direction) extends from -5 to 5 on the y-axis, giving it a length of 10. Therefore, the length of the semi-major axis is 5. - The semi-minor axis (along the x-direction) extends from -2 to 2 on the x-axis, giving it a length of 4. Therefore, the length of the semi-minor axis is 2. **Equation Form:** The equation of an ellipse centered at the origin, with a semi-major axis along the y-axis and a semi-minor axis along the x-axis, is given by: \[ \frac{x^2}{b^2} + \frac{y^2}{a^2} = 1 \] Where: - \(a\) is the semi-major axis length (5). - \(b\) is the semi-minor axis length (2). **Plugging in the Values:** \[ \frac{x^2}{2^2} + \frac{y^2}{5^2} = 1 \] This simplifies to: \[ \frac{x^2}{4} + \frac{y^2}{25} = 1 \] Thus, the equation of the ellipse is: \[ \frac{x^2}{4} + \frac{y^2}{25} = 1 \]
Expert Solution
Check Mark
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
See solutionCheck out a sample Q&A here
Step 1: We will analysis the given questions
VIEW
Step 2: Detailed solution
VIEW
Solution
VIEW
bartleby

Step by stepSolved in 3 steps with 2 images

See solution
Check out a sample Q&A here
Blurred answer
Knowledge Booster
Background pattern image
Similar questions
Recommended textbooks for you
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning
Text book image
Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
Text book image
Precalculus
Calculus
ISBN:9780135189405
Author:Michael Sullivan
Publisher:PEARSON
Text book image
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
SEE MORE TEXTBOOKS