Answer:
The center is located at (2, –1).
The major axis is 8 units long.
The vertices are 4 units above and below the centre.
The foci are √7 units above and below the centre.
Step-by-step explanation:
Assume the ellipse looks like the one below.
The properties of a vertical ellipse are
A. Centre
TRUE. The centre is at (2,-1).
B. Major axis
TRUE
Length of major axis = 3 - (-5) = 3 + 5 = 8
C. Minor axis
False
Length of minor axis = 5 - (-1) = 5 + 1 = 6
D. Vertices
TRUE
Distance between vertices = 8 = 2a
a - 8/2 = 4
Vertices at (h, k ± a) = (2, -1 ± 4)
E. Foci
TRUE
c² = a² - b² = 4² - 3² = 16 - 9 = 7
c = √7
The foci are √7 above and below the centre.
F. Foci
False.
The foci are on a vertical line.
