8. Consider the ellipse centered at (2,-1) with axes as shown in the figure below.

Its equation is: 

A. 4x2+y2+16x2y+13 = 0

B. x2+4y2-4x+8y+4 = 0

C. x2+4y2+4x8y+4 = 0

D. 4x2+y2-16x2y+13 = 0

E. 4x2+y2-16x+2y+13 = 0

 

Solution: The answer is E

The general form of the equation of an ellipse with, a vertical major axis, center (h,k), and major and minor axes of length 2a and 2b respectively, where a > b > 0 is given by,

From the graph above, notice that the major axis length, 2a = 4, and that the minor axis length, 2b = 2. Hence, a = 2 and b = 1. Since the center is (2,-1), then the equation of the given ellipse is,

Which simplifies to,