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Reviewed CSCA Mathematics question · Hard

A hyperbola centered at the origin has a vertex at (0, -5) and a focus at (0, -13). What is the length of its conjugate axis?

  1. 10
  2. 24
  3. 26
  4. 12
Show the answer and explanation

Correct answer

B. 24

Principle or equation

For a vertical hyperbola, c^2 = a^2 + b^2, where a is the distance from center to vertex and c is the distance to focus. The conjugate axis length is 2b.

Why this answer is correct

Here a = 5, c = 13. Then b^2 = c^2 - a^2 = 169 - 25 = 144, so b = 12. Conjugate axis length = 2b = 24.

Example

If vertex at (0,3) and focus at (0,5), then b = 4, conjugate axis = 8.

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