Expert: Sherman D. - 12/4/2004

Question
find the ellipse's standard-form equation from the given information about the foci and the vertices centered at the origin of the xy-plane.

1) foci: (sqrt of 2, 0)
  Vertices: (+-2,0)

Answer
Center : (0,0)
Vertices: (a,0) (-a,0)
Foci: (c,0) (-c,0)

Center : (0,0)
Vertices : (2,0) and (-2,0)
foci : (sqrt(2),0) and (-sqrt(2),0)

c^2 = a^2 - b^2
c = sqrt(a^2 - b^2)
sqrt(2) = sqrt((±2)^2 - b^2)
(±2)^2 - b^2 = 2
4 - b^2 = 2
-b^2 = -2
b^2 = 2
b = sqrt(2)

((x^2)/(a^2)) + ((y^2)/(b^2)) = 1
((x^2)/((±2)^2))) + ((y^2)/((±sqrt(2))^2) = 1

((x^2)/4) + ((y^2)/2) = 1

Look for the words "Basic Equations, Constants and Values of the Ellipse"

found at www.valleyview.k12.oh.us/vvhs/dept/math/ellipseguide.html