Question 847583
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Hi
major axis: 2a = 16, a = 8
(-5,1) and (3,1);   and 8/2 = 4, foci distance from center 
 {{{16 = 64 -b^2}}}  b^2 = 48
{{{(x+1)^2/64 + (y -1)^2/48= 1}}} 
{{{drawing(300,300,  -20,20,-20,20, arc(-1,1, 16, 13.86),
 grid(1),
circle(-5, 1,0.4),
circle(3, 1,0.4),
circle(-1, 1,0.4),
graph( 300, 300, -20,20,-20,20))}}}


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
 and ±{{{sqrt(a^2-b^2)}}}are the foci distances from center: a > b