SOLUTION: Given the equation (x+3)^2/36+(y-1)^2/18=1
find: the center. I found (-3,1)
vertices (-3.-5) and (-3,7)
the end points of minor axis I only came up with 6 radical 2
the foci I
Algebra.Com
Question 716150: Given the equation (x+3)^2/36+(y-1)^2/18=1
find: the center. I found (-3,1)
vertices (-3.-5) and (-3,7)
the end points of minor axis I only came up with 6 radical 2
the foci I got 3 radical 2 and length of major axis is 12
Are these correct?
I can't find the length of focal cord or its endpoints.
Please help
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You got the center in the right place. But the vertices are at the ends of the major axis. With the absence of an 
term in the equation, the major axis lines up with the 
axis when the denominator in the term is larger than the denominator in the 
term. 36 is bigger than 18, so the major axis has to be horizontal. -3 - 6 is -9, so one of your vertices is at (-9,1) and -3 + 6 = 3, so the other vertex is at (3,10).
As for the endpoints of the minor axis, take the square root of the smaller denominator. Since 18 is 9 times 2, the square root of 18 is 
. So your endpoints are )
and )
.
Since 
, the focal distance, 
, is the distance from the center to the focus, and the foci lie on the major axis, so the foci are at: )
and )
The semi-major axis is 6, so the major axis has to be 12.
The measure of the semi-latus rectum (i.e. half of the focal chord) is given by 
or in your case, 
. Hence the length of the focal chord is 6.
The latus rectum, or focal chord if you will, is perpendicular to the major axis at the focus. So for your ellipse, the left hand focal chord has end points (-9,4) and (-9,-2). I'll leave the endpoints of the other focal chord in your capable hands.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
Find the vertices, foci, and minor axis: (x-1)^2/21 + (y-3)^2/4 =... (answered by ewatrrr,Edwin McCravy)
Can you help me find the center, foci, vertices, length of the major and minor axis of... (answered by lwsshak3)
locate the center, foci, vertices, and ends of the latera recta of the ellipse. find the... (answered by KMST)
Vertices at (-2,-3) and (8,-3), one end of the minor axis at... (answered by lwsshak3)
Complete for the given equation as directed. (x-3)2/9+(y-6)2/16=1 Center (, ) Length of... (answered by lwsshak3)
For the given ellipse, find the principal axis, center, vertices, co-vertices, foci,... (answered by Edwin McCravy)
Find the vertices, foci, and minor axis.
x^2/36 + y^2/16 =... (answered by ewatrrr)
Find the end points of the minor and major axis for the graph of the ellipse... (answered by ikleyn,MathLover1)
How do I identify the center, co-vertices, foci, length of major axis, length of minor... (answered by lwsshak3)
