Problem 18 - Entrance Test

What is the equation of the ellipse with center (0, 0), major axis 10, and minor axis 6?

A. (x^2 / 25) + (y^2 / 9) = 1B. (x^2 / 9) + (y^2 / 25) = 1C. (x^2 / 25) + (y^2 / 16) = 1D. (x^2 / 16) + (y^2 / 25) = 1

Correct: A

The general equation of an ellipse with center (0, 0) is (x^2 / a^2) + (y^2 / b^2) = 1, where 2a is the length of the major axis and 2b is the length of the minor axis. Given the major axis is 10, a = 10 / 2 = 5. Given the minor axis is 6, b = 6 / 2 = 3. So, the equation of the ellipse is (x^2 / 5^2) + (y^2 / 3^2) = 1, (x^2 / 25) + (y^2 / 9) = 1.