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Reviewed CSCA Mathematics question · Easy

A hyperbola centered at the origin has a vertex at (0, 3) and a focus at (0, 5). What is the length of its transverse axis?

  1. 4
  2. 6
  3. 8
  4. 10
Show the answer and explanation

Correct answer

B. 6

Principle or equation

For a hyperbola centered at the origin with vertical transverse axis, the vertices are at (0, ±a) and foci at (0, ±c), where c^2 = a^2 + b^2. The transverse axis length is 2a.

Why this answer is correct

The vertex is at (0, 3), so a = 3. The focus is at (0, 5), so c = 5. The transverse axis is the segment connecting the two vertices, length 2a = 2*3 = 6.

Example

If a hyperbola has vertices at (±2, 0) and foci at (±3, 0), the transverse axis length is 4.

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