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The graph of an ellipse is given. Match the graph to its equation. 6- -6 ..... Choose the correct equation below. x? y? O B. x? = 1 25 DA. = 1 + 25 16 c. 25 +y? =- x? y? = 1 25 16

The graph of an ellipse is given. Match the graph to its equation. 6- -6 ..... Choose the correct equation below. x? y? O B. x? = 1 25 DA. = 1 + 25 16 c. 25 +y? =- x? y? = 1 25 16

Calculus: Early Transcendentals
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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**Ellipse Graph and Equation Matching** The graph of an ellipse is shown on a coordinate plane with the x-axis and y-axis both ranging from -6 to 6. The ellipse is centered at the origin (0,0) with its major axis along the y-axis and minor axis along the x-axis. The length of the semi-major axis is 6 units (vertically) and the length of the semi-minor axis is 4 units (horizontally). **Graph Details:** - The ellipse is elongated vertically. - The semi-major axis (vertical) length is 6. - The semi-minor axis (horizontal) length is 4. **Equation Options:** Choose the correct equation that represents the given ellipse: A. \(\frac{x^2}{25} + \frac{y^2}{16} = 1\) B. \(\frac{x^2}{16} + \frac{y^2}{25} = 1\) C. \(\frac{x^2}{25} + y^2 = 1\) D. \(\frac{x^2}{16} + \frac{y^2}{25} = 1\) **Explanation:** An ellipse centered at the origin with vertical major axis has the standard form \(\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1\), where \(a\) is the semi-major axis and \(b\) is the semi-minor axis. - Here, \(a = 6\) and \(b = 4\). The correct equation matching the graph is: B. \(\frac{x^2}{16} + \frac{y^2}{36} = 1\) Note: The nearest correct match, based on the answers provided, would directly correspond to the given axis lengths, even if the options differ slightly in numbers; proper graph values would use \(36\) and \(16\), consistent with the graph.
Transcribed Image Text:**Ellipse Graph and Equation Matching** The graph of an ellipse is shown on a coordinate plane with the x-axis and y-axis both ranging from -6 to 6. The ellipse is centered at the origin (0,0) with its major axis along the y-axis and minor axis along the x-axis. The length of the semi-major axis is 6 units (vertically) and the length of the semi-minor axis is 4 units (horizontally). **Graph Details:** - The ellipse is elongated vertically. - The semi-major axis (vertical) length is 6. - The semi-minor axis (horizontal) length is 4. **Equation Options:** Choose the correct equation that represents the given ellipse: A. \(\frac{x^2}{25} + \frac{y^2}{16} = 1\) B. \(\frac{x^2}{16} + \frac{y^2}{25} = 1\) C. \(\frac{x^2}{25} + y^2 = 1\) D. \(\frac{x^2}{16} + \frac{y^2}{25} = 1\) **Explanation:** An ellipse centered at the origin with vertical major axis has the standard form \(\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1\), where \(a\) is the semi-major axis and \(b\) is the semi-minor axis. - Here, \(a = 6\) and \(b = 4\). The correct equation matching the graph is: B. \(\frac{x^2}{16} + \frac{y^2}{36} = 1\) Note: The nearest correct match, based on the answers provided, would directly correspond to the given axis lengths, even if the options differ slightly in numbers; proper graph values would use \(36\) and \(16\), consistent with the graph.
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