Equation for the ellipse

[TonyC]

How would I go about finding the standard equation for the ellipse, using eithter the giver characteristics, or characteristics taken from the graph.
vertices: (0, +8) ; foci: (0, +2 sq rt15) :?:

 

[tkhunny]

How would I go about finding the standard equation for the ellipse, using eithter the giver characteristics, or characteristics taken from the graph.
vertices: (0, +8) ; foci: (0, +2 sq rt15) :?:

First, just write it down.

(x-h)²/a² + (y-k)²/b² = 1

Then fill in the parts you can see. The center is exactly between the foci or the vertices. This puts it at the Origin, (0,0), making h = 0 and k = 0, leaving:

x²/a² + y²/b² = 1

You should have a relationship between 'a' and 'b' and 'c'. 2*a is the distance between the vertices on the major axis. 2*c is the distance between the foci. 2*b is the distance between the vertices on the minor axis. b² = a² - c². You have a = 8 and c = 2*sqrt(15).

Where does that leave you?

 

[TonyC]

:idea: I see the light!