SOLUTION: I need help with this question, I keep coming up with the wrong answers. The equation of the ellipse that has a center at (8,2) , a focus at (11,2) , and a vertex at (13,2) , is

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I need help with this question, I keep coming up with the wrong answers. The equation of the ellipse that has a center at (8,2) , a focus at (11,2) , and a vertex at (13,2) , is      Log On


   

Question 1000242: I need help with this question, I keep coming up with the wrong answers.
The equation of the ellipse that has a center at (8,2) , a focus at (11,2) , and a vertex at (13,2) , is
(x−C)^2/ A^2 +(y−D)^2/ B^2 =1
where
A= 4
B= 6
C= 8
D= 2


2. The equation of the ellipse that has a center at (1,5) , a focus at (5,5) , and a vertex at (−4,5) , is
(x−C)^ 2/ A^2 +(y−D)^2/ B ^2 =1
where
A= 5
B= 4
C= 1
D= 5


Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Difficult to make the right kind of drawing here, but try making a sketch of the ellipse as described.


Distance from center (8,2) to a vertex (13,2) is A=13-8=5, so highlight%28A=5%29.

Use the variable C as the distance from the center to either focus. Your exercise description
will mean that you have C=3.

You want to find B. The fact relating A, B, and C using C as the distance from center
to either focus, is B%5E2%2BC%5E2=A%5E2, giving B%5E2=A%5E2-C2.
Evaluate the value for B^2.
-
B%5E2=A%5E2-C%5E2
B%5E2=5%5E2-3%5E2
B%5E2=25-9
highlight%28B%5E2=16%29

The standard form equation %28Y-k%29%5E2%2FB%5E2%2B%28X-h%29%5E2%2FA%5E2=1 can now be filled-in, giving you
highlight%28highlight%28%28X-8%29%5E2%2F25%2B%28Y-2%29%5E2%2F16=1%29%29.