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xxfamousxx91
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Homework Statement
How do you know whether you restrict the domain or range with a horizontal ellipse ?
Homework Equations
x^2/49 +y^2/10=1
Restricting Domain and Range in broken conics
- Thread starter xxfamousxx91
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SUMMARY
The discussion focuses on determining the restrictions of domain and range for the horizontal ellipse defined by the equation x²/49 + y²/10 = 1. The analysis concludes that the domain is restricted to -7 ≤ x ≤ 7, as this is the maximum extent of x when y equals 0. Conversely, the range is restricted to -√10 ≤ y ≤ √10, since y² cannot exceed 10 when x is not zero. These conclusions are derived from evaluating the ellipse's equation and understanding the implications of its geometric properties.
PREREQUISITES- Understanding of conic sections, specifically ellipses.
- Knowledge of algebraic manipulation and solving equations.
- Familiarity with the Cartesian coordinate system.
- Basic concepts of domain and range in functions.
- Study the properties of horizontal and vertical ellipses in conic sections.
- Learn how to graph ellipses using standard equations.
- Explore the implications of domain and range restrictions in other conic sections.
- Investigate the relationship between the coefficients in the ellipse equation and its geometric characteristics.
Students studying algebra and geometry, particularly those focusing on conic sections and their properties. This discussion is also beneficial for educators teaching these concepts in a classroom setting.
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