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What are the foci of the ellipse represented by the equation x²/9 + y²/4 = 1?

A) (√13, 0)
B) (√5, 0)
C) (0, √5)
D) None of the above

User Jeninne
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1 Answer

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Final answer:

The foci of the ellipse defined by x²/9 + y²/4 = 1 are at (√5, 0) and (-√5, 0) because the distance c is the square root of 5, derived from the formula c² = a² - b² where a is the length of the semi-major axis and b is the length of the semi-minor axis.

Step-by-step explanation:

The foci of the ellipse represented by the equation x²/9 + y²/4 = 1 can be found using the relationship c² = a² - b², where c is the distance from the center to each focus, a is the semi-major axis, and b is the semi-minor axis of the ellipse.

In this equation, is larger than , so the semi-major axis is the square root of 9 (which is 3), and the semi-minor axis is the square root of 4 (which is 2). Thus, is 3² - 2², which equals 9 - 4, therefore is 5. The distance c is then the square root of 5, giving us the foci located at (√5, 0) and (-√5, 0).

So, the correct answer is B) (√5, 0).

User Seaky Lone
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