CSCAPrep
Reviewed CSCA Mathematics question · Hard

An ellipse has its center at the origin, a focus at (0, 4), and a vertex at (0, 5). What is the length of the minor axis?

  1. 6
  2. 8
  3. 10
  4. 12
Show the answer and explanation

Correct answer

A. 6

Principle or equation

For an ellipse centered at the origin with vertical major axis, 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. The length of the minor axis is 2b.

Why this answer is correct

The vertex at (0,5) gives a = 5. The focus at (0,4) gives c = 4. Then b^2 = a^2 - c^2 = 25 - 16 = 9, so b = 3. The minor axis length is 2b = 6.

Example

For an ellipse with a=10 and c=6, b^2=100-36=64, b=8, minor axis=16.

This published item includes a stored explanation and passed the platform’s publication workflow. It is independent preparation material, not a claim of an official or recalled examination question.

Related practice questions

Easy · Geometry and algebraWhat is the product (2 + 3i)(1 - i)?Standard · Geometry and algebraWhat is the center of the circle given by x^2 + y^2 - 4x + 6y - 3 = 0?Easy · Geometry and algebraGiven vectors u = (3, -2) and v = (1, 4), what is 2u - v?Easy · Geometry and algebraA rectangular box has vertices at (0,0,0), (4,0,0), (0,3,0), and (0,0,12). What is the length of the space diagonal of this box?Standard · Geometry and algebraWhat is the value of (3 + 2i) / (1 - i)?