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 x28+y24=1\frac{x^2}{8} + \frac{y^2}{4} = 1, with the foci marked at (±2,0)(\pm 2, 0). 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:

  1. How does changing the values of a2a^2 and b2b^2 affect the shape of an ellipse?
  2. What happens if a=ba = b in an ellipse equation?
  3. Can you explain how eccentricity impacts the shape of the ellipse?
  4. How do you calculate the area of an ellipse?
  5. 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