An ellipse has its center at the origin, a focus at (0, -√5), and a vertex at (0, -3). What is the length of its major axis?
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Correct answer
B. 6
Principle or equation
For an ellipse centered at the origin with vertical major axis, the standard form is x^2/b^2 + y^2/a^2 = 1, where a > b > 0. The distance from the center to a focus is c, with c^2 = a^2 - b^2. The vertices are at (0, ±a), so the given vertex (0, -3) gives a = 3. The length of the major axis is 2a.
Why this answer is correct
The vertex is at (0, -3), so a = 3. The major axis length is 2a = 6. The focus information is consistent: c = √5, so b^2 = a^2 - c^2 = 9 - 5 = 4, b = 2, but it is not needed for the major axis length.
Example
For an ellipse with vertex at (0, 5) and focus at (0, 3), a = 5, major axis length = 10.
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