Answer :
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
[tex]\textbf{Vertical ellipse}\\\dfrac{ (x - h)^{2} }{b^{2}} + \dfrac{(y - k)^{2}}{a^{2}} = 1\begin{cases}\text{Centre} = (h,k)\\\text{Dist. between vertices} = 2a\\\text{Vertices} = (h, k\pm a)\\\text{Dist. between covertices} = 2b\\ \text{Covertices}= (h\pm b, k)\\c = \sqrt{a^{2} - b^{2}}\\\text{Dist. of foci from centre} = c\\\text{Foci} = (h, k\pm c)\\\end{cases}[/tex]
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.
