SOLUTION: Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: (0, ±8); foci: (0, ±6)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: (0, ±8); foci: (0, ±6)      Log On


   

Question 759157: Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.
Vertices: (0, ±8); foci: (0, ±6)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The (main) vertices give you 'a', and the foci give you 'c'. You use a and c to get an expression, and then a value for b.

Making a drawing and showing a triangle so one side is b, another side is c, the hypotenuse is a.
a%5E2=b%5E2%2Bc%5E2
b%5E2=a%5E2-c%5E2
and based on what you are given,
b%5E2=8%5E2-6%5E2
b%5E2=28

The center of the ellipse is the origin, so the equation is
highlight%28x%5E2%2F8%5E2%2By%5E2%2F28=1%29