Math Problem Statement

What is the length of the minor axis of the ellipse below?

Solution

The ellipse shown in the image is vertically oriented, meaning the major axis is along the y-axis, while the minor axis is along the x-axis.

In standard form, the equation of an ellipse is:

x2b2+y2a2=1\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1

where aa is the semi-major axis, and bb is the semi-minor axis.

From the graph:

  • The ellipse extends from y=10y = -10 to y=10y = 10, so the total length of the major axis is 20. Therefore, the semi-major axis a=10a = 10.
  • The ellipse extends from x=2x = -2 to x=2x = 2, so the total length of the minor axis is 4. Therefore, the semi-minor axis b=2b = 2.

The length of the minor axis is twice the value of bb, which is:

Minor Axis Length=2×2=4\text{Minor Axis Length} = 2 \times 2 = 4

Thus, the correct answer is 4.

Would you like further details or clarification? Here are 5 related questions to explore this concept further:

  1. How do you determine whether an ellipse is vertically or horizontally oriented?
  2. What is the formula for the eccentricity of an ellipse?
  3. How would you calculate the area of the ellipse shown in the graph?
  4. Can you derive the equation of the ellipse using its dimensions from the graph?
  5. What are the differences between ellipses and circles in terms of their geometric properties?

Tip: The major and minor axes help identify key properties of an ellipse, including its shape and orientation.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Ellipses
Geometry
Graph Interpretation

Formulas

Ellipse equation: (x^2 / b^2) + (y^2 / a^2) = 1

Theorems

Properties of Ellipses
Symmetry of Ellipses

Suitable Grade Level

Grades 9-11