Consider ellipse x^2/16 + y^2/9 = 1. Which statement about a, b, c and foci is true?

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Multiple Choice

Consider ellipse x^2/16 + y^2/9 = 1. Which statement about a, b, c and foci is true?

Explanation:
In this ellipse, the equation is in the form x^2/a^2 + y^2/b^2 = 1 with a ≥ b, so the major axis is horizontal. The semi-major axis is a = sqrt(16) = 4 and the semi-minor axis is b = sqrt(9) = 3. The distance from the center to each focus is c, where c^2 = a^2 − b^2 = 16 − 9 = 7, so c = sqrt(7). The foci are at (±c, 0) along the major axis, giving (±√7, 0). This matches a = 4, b = 3, c^2 = 7, and foci at (±√7, 0).

In this ellipse, the equation is in the form x^2/a^2 + y^2/b^2 = 1 with a ≥ b, so the major axis is horizontal. The semi-major axis is a = sqrt(16) = 4 and the semi-minor axis is b = sqrt(9) = 3. The distance from the center to each focus is c, where c^2 = a^2 − b^2 = 16 − 9 = 7, so c = sqrt(7). The foci are at (±c, 0) along the major axis, giving (±√7, 0).

This matches a = 4, b = 3, c^2 = 7, and foci at (±√7, 0).

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