An ellipse has its center at the origin, a focus at (4, 0), and a vertex at (5, 0). What is the length of its minor axis?
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Correct answer
A. 6
Principle or equation
For an ellipse centered at the origin with major axis along the x-axis, the relationship is c^2 = a^2 - b^2, where a is the semi-major axis, b is the semi-minor axis, and c is the distance from center to focus.
Why this answer is correct
The vertex at (5,0) gives a = 5. The focus at (4,0) gives c = 4. Then b^2 = a^2 - c^2 = 25 - 16 = 9, so b = 3. The minor axis length is 2b = 6.
Example
If a = 5 and c = 3, then b = 4 and minor axis = 8.
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