Math Problem Statement
Graph the ellipse. 𝑥ଶ 4 + 𝑦ଶ 49 = 1
Solution
Here is the graph of the ellipse represented by the equation:
Summary of Key Features:
- Center: (0, 0)
- Major Axis (along the y-axis): Length = 14
- Minor Axis (along the x-axis): Length = 4
Let me know if you need more details or explanations!
Here are some related questions for deeper understanding:
- How do you determine whether the major axis is along the x-axis or y-axis?
- What is the relationship between the lengths of the axes and the equation?
- How would the graph change if and were swapped?
- How do you calculate the foci of an ellipse?
- How does an ellipse differ from a circle mathematically?
Tip: In ellipses, the larger denominator corresponds to the major axis.
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Math Problem Analysis
Mathematical Concepts
Conic Sections
Ellipses
Coordinate Geometry
Formulas
Standard form of an ellipse: (x^2/a^2) + (y^2/b^2) = 1
Length of the major axis: 2b
Length of the minor axis: 2a
Theorems
Definition of an ellipse: the set of all points such that the sum of the distances from two foci is constant.
Suitable Grade Level
Grades 10-12