8. Consider the ellipse centered at (2,-1) with axes as shown in the figure below.
Its equation is:
|
A. 4x2+y2+16x–2y+13 = 0 |
B. x2+4y2-4x+8y+4 = 0 |
C. x2+4y2+4x–8y+4 = 0 |
|
D. 4x2+y2-16x–2y+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,
