An ellipse has its center at the origin, a focus at (3, 0), and a vertex at (5, 0). What is the length of its minor axis?
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Correct answer
B. 8
Principle or equation
For an ellipse centered at origin with major axis along x-axis: c^2 = a^2 - b^2, where a is semi-major axis, c is focal distance, b is semi-minor axis. Length of minor axis = 2b.
Why this answer is correct
Given focus (3,0) => c=3; vertex (5,0) => a=5. Then b^2 = a^2 - c^2 = 25 - 9 = 16 => b=4. Minor axis length = 2b = 8.
Example
If a=10, c=6, then b=8, minor axis=16.
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