SOLUTION: Write the standard form of an ellipse given the following.\ Vertices: (-2,16) and (-2,-6) Foci: (-2,5+sqrt(57)) and (-2,5-sqrt(57))

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write the standard form of an ellipse given the following.\ Vertices: (-2,16) and (-2,-6) Foci: (-2,5+sqrt(57)) and (-2,5-sqrt(57))      Log On


   

Question 1023160: Write the standard form of an ellipse given the following.\
Vertices: (-2,16) and (-2,-6)
Foci: (-2,5+sqrt(57)) and (-2,5-sqrt(57))
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The center of the ellipse would be (-2,5). The semi-major axis is a = 11 (=%2816--6%29%2F2+). The focal length is c = %285%2Bsqrt%2857%29%29+-+5+=+sqrt%2857%29.
==> b%5E2+=+a%5E2+-+c%5E2+=+11%5E2+-+%28sqrt%2857%29%29%5E2+=+121-57+=+65
==> the standard form is %28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2+=+1, or
highlight%28%28x%2B2%29%5E2%2F65%2B%28y-5%29%5E2%2F121+=+1%29