SOLUTION: Write the equation of each ellipse or hyperbola. 13. A vertical ellipse has a focus (−6,1). It has a co-vertex of (-10, -7) The correct answer is: {{{((x+6)^2)/16 + ((y+7)^2

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write the equation of each ellipse or hyperbola. 13. A vertical ellipse has a focus (−6,1). It has a co-vertex of (-10, -7) The correct answer is: {{{((x+6)^2)/16 + ((y+7)^2      Log On


   



Question 1158928: Write the equation of each ellipse or hyperbola.
13. A vertical ellipse has a focus (−6,1). It has a co-vertex of (-10, -7)
The correct answer is:
%28%28x%2B6%29%5E2%29%2F16+%2B+%28%28y%2B7%29%5E2%29%2F80+=+1
However, I do not know how to do the work to get the answer

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

A vertical ellipse has a focus (-6,1). It has a co-vertex of (-10, -7)
formula for ellipse a vertical is:

%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1


co-vertex (h-b,k) and (h%2Bb,k)
if one co-vertex of (-10, -7), then =>
h-b=-10, k=-7

focus is at (h,k%2Bc) and (h,k-c)
if one focus (-6,1) , then
h=-6,
k%2Bc=1, ->since k=-7
-7%2Bc=1
c=8
the other one focus is at
(-6,-7-8)=(-6,-15)

The center is half way between, at (-6, -7)
since
h-b=-10 and h=-6=> -6-b=-10 =>-6%2B10=b->
b=4
other co-vertex is at (h%2Bb,k)=(-6-4,-7)=(-2,-7)
find a
c%5E2=a%5E2-b%5E2
8%5E2=a%5E2-4%5E2
a%5E2=64%2B16
a%5E2=80
and your equation is:
%28x%2B6%29%5E2%2F16%2B%28y%2B7%29%5E2%2F80=1