Question 930815
 Standard Form of an Equation of an Ellipse is {{{(x-h)^2/a^2 + (y-k)^2/b^2 = 1 }}} 
where Pt(h,k) is the center. (a variable positioned to correspond with major axis)
 a and b  are the respective vertices distances from center.
 The foci distances from center:   c = ±{{{sqrt(a^2-b^2)}}} where  a > b
eccentricity = c/a
.........
4x^2+25y^2=100 
{{{x^2/5^2 + y^2/2^2 = 1}}} C(0,0)
V(5,0),V(-5,0) & V(0,2),V(0,-2)
c =√(25 - 4) = √(21)
eccentricity = √21/5
{{{drawing(300,300,   -10,10,-10,10,  arc(0,0,10,4), 
 grid(1),

graph( 300, 300, -10,10,-10,10,0 ))}}}

..........
x^2/16+y^2/25=1
{{{x^2/4^2 + y^2/5^2 = 1}}}  C(0,0)
 & V(4,0),V(-4,0) & V(0,5),V(0,-5)

 c =√(25 - 16) = 3
eccentricity = 3/5
{{{drawing(300,300,   -10,10,-10,10,  arc(0,0,8,10), 
 grid(1),
graph( 300, 300, -10,10,-10,10,0 ))}}}
........
1/2x^2+1/8y^2=1/4 
2x^2 + y^2/4 = 1
{{{x^2/(sqrt(1/2))^2 + y^2/ 2^2 = 1}}}
.........
y^2=1-2x^2 
2x^2 + y^2 = 1
{{{ x^2/(sqrt(1/2))^2 + y^2/1^2 = 1}}}
.......
X^2+4y^2=16
{{{x^2/4^2 + y^2/2^2 = 1}}}