Question 441859
  <pre><font face = "Tohoma" size = 4 color = "indigo"><b> 
Hi
Ellipse, foci at (-4,2) and (-4,8), vertex at (-4,10) 
Major axis along x = -4  f = (8-2)/2 = 6/2 = 3 = sqrt(b^2-a^2) C(-4,5) b = 5
                                             3 = sqrt(25-a^2) a^2 = 16
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 and a and b  are the respective vertices distances from center.
  (x+4)^2/16 + (y-5)^2/25 = 1
{{{drawing(300,300,  -15,15,-15,15,  arc(-4,5,8,10), grid(1),
circle(-4, 8,0.3),
circle(-4, 2,0.3),
circle(-4, 10,0.3),
graph( 300, 300, -15,15,-15,15 ))}}}




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