Question 1204150: Find the end points of the minor and major axis for the graph of the ellipse
{(x-4)^2/9} + {(y-3)^2/25} = 1
a. Maximum point on the major axis:
b. Minimum point on the major axis:
c. Maximum point on the minor axis:
d. Minimum point on the minor axis:
e. Maximum focal point:
f. Minimum focal point:
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52786)   (Show Source):
You can put this solution on YOUR website! .
The center is at the point (x,y) = (4,3).
Major semi-axis is of the length of  = 5 from the center vertically.
Minor semi-axis is of the length of  = 3 from the center horizontally.
So, you just can answer (a), (b), (c), and (d) on your own.
Focal points are at the distance  =  = 4 from the center vertically, up and down.
Having it, you can answer (e) and (f) on your own.
Solved.
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Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website! The standard form you need is:
where:
 = the length of the major axis (vertical)
 = the length of the minor axis (horizontal)
( , ) = center of ellipse
you are given:
Therefore:
 , 
 , 
 ,
C(,) = ( , )
The coordinates of the endpoints of the major axis are: (,± ) or (, ), (, )
a. Maximum point on the major axis:(,)
b. Minimum point on the major axis:(,)
The coordinates of the endpoints of the minor axis are: (±,) or ( ,), ( ,)
c. Maximum point on the minor axis: (,)
d. Minimum point on the minor axis: (,)
e. Maximum focal point:
f. Minimum focal point:
Focal points are at the distance  from the center vertically, up and down
so, foci are
(, )= (,) above center
and
(, )= (, ) below center
e. Maximum focal point: (,)
f. Minimum focal point: (,)
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