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Choose the correct conic section to fit the equation. (x - 3)�� (y - 2)�� = 16

1) parabola
2) ellipse
3) circle
4) hyperbola

1 Answer

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Final answer:

The equation represents an ellipse, which is a closed curve formed by the intersection of a plane with a cone.

Step-by-step explanation:

The given equation, (x - 3)² (y - 2)² = 16, represents an ellipse.

An ellipse is a closed curve formed by the intersection of a plane with a cone. The general equation of an ellipse is (x-h)²/a² + (y-k)²/b² = 1, where (h,k) are the coordinates of the center and a and b are the lengths of the semi-major and semi-minor axes, respectively.

In this case, the equation can be written as (x-3)²/4 + (y-2)²/4 = 1, indicating that the center is at (3,2) with semi-major and semi-minor axes of length 2. Therefore, the correct conic section for the given equation is an ellipse.

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