Math Problem Statement
Solution
The ellipse shown in the image is vertically oriented, meaning the major axis is along the y-axis, while the minor axis is along the x-axis.
In standard form, the equation of an ellipse is:
where is the semi-major axis, and is the semi-minor axis.
From the graph:
- The ellipse extends from to , so the total length of the major axis is 20. Therefore, the semi-major axis .
- The ellipse extends from to , so the total length of the minor axis is 4. Therefore, the semi-minor axis .
The length of the minor axis is twice the value of , which is:
Thus, the correct answer is 4.
Would you like further details or clarification? Here are 5 related questions to explore this concept further:
- How do you determine whether an ellipse is vertically or horizontally oriented?
- What is the formula for the eccentricity of an ellipse?
- How would you calculate the area of the ellipse shown in the graph?
- Can you derive the equation of the ellipse using its dimensions from the graph?
- What are the differences between ellipses and circles in terms of their geometric properties?
Tip: The major and minor axes help identify key properties of an ellipse, including its shape and orientation.
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Math Problem Analysis
Mathematical Concepts
Ellipses
Geometry
Graph Interpretation
Formulas
Ellipse equation: (x^2 / b^2) + (y^2 / a^2) = 1
Theorems
Properties of Ellipses
Symmetry of Ellipses
Suitable Grade Level
Grades 9-11