Final answer:
The conic section described by the equation (x + 2)^2 /16 + (y−9)^2 /36 = 1 is C. an ellipse.
Step-by-step explanation:
The conic section described by the equation (x + 2)^2 /16 + (y−9)^2 /36 = 1 is an ellipse. This equation is in the general form of an ellipse, where the terms are divided by two different constants, and the sum of the fractions equals 1. In an ellipse, the sum of the distances from any point on the ellipse to the two foci is constant, which is why its general equation has the sum of two squares, each divided by a constant, equal to 1.
If this equation represented a circle, the denominators of both fractions would be the same because a circle is a special case of an ellipse where the two axes are equal in length. A hyperbola would have a subtraction between the two fractions instead of addition, and a parabola would not be expressed as a ratio of two squared terms.