Question

Offering 20 points, identify the conic section from its equation (x-5)²/4 + (y+3)²/16 = 1.

A. Ellipse
B. Hyperbola
C. Parabola
D. Circle

Answer 1

The equation (x-5)²/4 + (y+3)²/16 = 1 represents an ellipse.

Step-by-step explanation:

The equation (x-5)²/4 + (y+3)²/16 = 1 represents an ellipse. An ellipse is a closed curve such that the sum of the distances from a point on the curve to the two foci is a constant. In this equation, the center of the ellipse is at the point (5,-3) and the lengths of the major and minor axes are 4 and 8, respectively. Therefore, the conic section represented by this equation is an ellipse.