Final answer:
The equation (x - 8)²/36 - (y + 18)²/361 = 1 represents an ellipse.
Step-by-step explanation:
The equation (x - 8)²/36 - (y + 18)²/361 = 1 represents an ellipse.
An ellipse is a conic section that is formed by the intersection of a plane with a cone. It has a characteristic shape where the distance from the center to any point on the ellipse is always a constant ratio to the distance from the center to another point on the ellipse. In the given equation, the terms (x - 8)²/36 and (y + 18)²/361 are in the form (x - h)²/a² + (y - k)²/b² = 1, which is the standard form of an ellipse.
To identify the shape of a conic section, we look at the ratios of the coefficients of the x and y terms. In this equation, since the coefficients are equal (36/361), the ellipse is not skewed or tilted, it is a circle or a stretched circle with a ratio of 6:19.