In ellipse x^2/25 + y^2/16 = 1, c^2 equals a^2 - b^2. What is c^2?

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Multiple Choice

In ellipse x^2/25 + y^2/16 = 1, c^2 equals a^2 - b^2. What is c^2?

Explanation:
For an ellipse aligned with the axes, the relationship c^2 = a^2 - b^2 holds, where a is the semi-major axis and b is the semi-minor axis. In the equation x^2/25 + y^2/16 = 1, the larger denominator is under x^2, so a^2 = 25 and b^2 = 16. Subtracting gives c^2 = 25 - 16 = 9. So c^2 is 9 (and the distance to a focus is c = 3).

For an ellipse aligned with the axes, the relationship c^2 = a^2 - b^2 holds, where a is the semi-major axis and b is the semi-minor axis. In the equation x^2/25 + y^2/16 = 1, the larger denominator is under x^2, so a^2 = 25 and b^2 = 16. Subtracting gives c^2 = 25 - 16 = 9. So c^2 is 9 (and the distance to a focus is c = 3).

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