Question 1045393
 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
vertices are at (3,-3) and (3,5) |major axis 8, Center: (3,1)  a = 4 
 minor axis is 6   | b = 3
{{{(x-3)^2/4^2 + (y-1)^2/3^2 = 1 }}} 
c = ±{{{sqrt(a^2-b^2)}}} , c = ±{{{sqrt(16-9)}}}  c = ± {{{sqrt(7)}}}
foci: (3, 1- {{{sqrt(7)}}})  and  (3, 1+ {{{sqrt(7)}}})
The directrices are a distance aČ/c in both directions from the center of the ellipse.
directrix: y = 1 + 16/{{{sqrt(7)}}})  and y = -3 - sqrt(7
{{{drawing(300,300,   -10,10,-10,10,   grid(1), arc(3,1,6,8), circle(3,1,0.3),
circle(3,-3, 0.3),
circle(3,5, 0.3),
circle(0,1, 0.3),
circle(6,1, 0.3),
circle(3,(1-sqrt(7)), 0.3),
circle(3,(1+sqrt(7)), 0.3),
graph( 300, 300,   -10,10,-10,10,  0, 1+16/sqrt(7), 1 - 16/sqrt(7) ) )}}}