SOLUTION: My problem says: find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse with the given equation. Then graph the ellipse. (x-8)

Question 406971: My problem says: find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse with the given equation. Then graph the ellipse.
(x-8) squared over 144 + (y-2) squared over 81 =1
I understand the center is (8,2) but I do not understand how to find the foci and the endpoints of the major and minor axes. Thank you so much, I appreciate it.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
My problem says: find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse with the given equation. Then graph the ellipse.(x-8) squared over 144 + (y-2) squared over 81 =1 I understand the center is (8,2) but I do not understand how to find the foci and the endpoints of the major and minor axes. Thank you so much, I appreciate it.
..
Standard forms of an ellipse:
(x-h)^2/a^2+(y-k)^2/b^2=1 (major axis horizontal)
(y-k)^2/a^2+(x-h)^2/b^2=1 (major axis vertical)
..
Given equation is of the first form:
(x-8)^2/144+(y-2)^2/81=1
This is an ellipse with a horizontal major axis with center(8,2)
a^2=144
a=12
b^2=81
b=9
c=sqrt(a^2-b^2)=sqrt(144-81)=sqrt(83)=9.11
Length of major axis=2a=24
Length of minor axis=2b=18
Measuring from the center(8,2), the endpoints
vertices =(8+-a,2)=(8+-12,2)=(20,2),(-4,2)
foci=(8+-c,2)=(8+-9.11,2)=(17.11,2),(-1.11,2)
minor axis=(8,2+-b)=(8,2+-9)=(8,11),(8,-7)
With data from above, your graph should look like the graph below:
..
2+(81-(81(x-8)^2)/144)^.5

RELATED QUESTIONS
I don't know how to do this problem Find the coordinates of the center and foci and the... (answered by stanbon)

Find the coordinates of the center and foci and the lengths of the major and minor axes... (answered by lynnlo)

How do you find the coordinates of the center and foci and the lengths of the major and... (answered by ewatrrr)

Find the center, vertices, foci, and the lengths of the major and minor axes of the... (answered by lwsshak3)

What is the center, foci, and the lengths of the major and minor axes for the ellipse,... (answered by Paul)

What is the center, foci, and the lengths of the major and minor axes for the ellipse,... (answered by venugopalramana)

What are the coordinates of the center, the lengths of the major and minor axes,... (answered by lwsshak3,MathLover1)