Math Problem Statement
x²/8 +y²/4 =1 find ellipse properties and graph
Solution
Here is the graph of the ellipse represented by the equation , with the foci marked at . The ellipse is wider along the x-axis due to the larger value of the semi-major axis.
Would you like any more details or have any questions?
Here are some related questions for further exploration:
- How does changing the values of and affect the shape of an ellipse?
- What happens if in an ellipse equation?
- Can you explain how eccentricity impacts the shape of the ellipse?
- How do you calculate the area of an ellipse?
- What are the properties of an ellipse when the foci coincide?
Tip: The distance between the foci and the center defines how "stretched" an ellipse is. The greater this distance, the more elongated the ellipse.
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Math Problem Analysis
Mathematical Concepts
Conic Sections
Ellipses
Coordinate Geometry
Formulas
Standard form of an ellipse: (x²/a²) + (y²/b²) = 1
Focal distance: c² = a² - b²
Semi-major axis (a)
Semi-minor axis (b)
Theorems
Ellipse definition based on distance from foci
Relationship between semi-major and semi-minor axes
Suitable Grade Level
Grades 10-12