Math Problem Statement

Graph the ellipse. 𝑥ଶ 4 + 𝑦ଶ 49 = 1

Solution

Here is the graph of the ellipse represented by the equation:

x24+y249=1\frac{x^2}{4} + \frac{y^2}{49} = 1

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:

  1. How do you determine whether the major axis is along the x-axis or y-axis?
  2. What is the relationship between the lengths of the axes and the equation?
  3. How would the graph change if a2a^2 and b2b^2 were swapped?
  4. How do you calculate the foci of an ellipse?
  5. 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