SOLUTION: 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

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(52788)   (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.

My congrats (!)

-------------------------

You may learn everything you need from my lesson
    - Ellipse definition, canonical equation, characteristic points and elements
in this site in short, clear and compact form.

Do not miss this happy and rare opportunity ( ! )

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: (,)

RELATED QUESTIONS
please help me I could never figure this out no matter how much I try. Thanks Find... (answered by stanbon)
Find the center, foci, vertices, length of major axis, and length of minor axis of the... (answered by Edwin McCravy)
Write an equation of an ellipse centered at the origin that has a horozontal axis of... (answered by solver91311)
For the following ellipse: (x + 2)2 + (y + 2)2 = 1 (answered by Boreal)
For the given ellipse, find the principal axis, center, vertices, co-vertices, foci,... (answered by Edwin McCravy)
Choose the equation that best represents the ellipse with center (�5, �2), horizontal... (answered by ewatrrr)
What is the center, foci, and the lengths of the major and minor axes for the ellipse,... (answered by Paul)
Find the coordinates of the foci, the endpoints of the major axis, minor axis and the... (answered by MathLover1)
Write an equation for each ellipse described below The foci are a (4,0) and (-4,0). Then (answered by lwsshak3)