Question 451202
  <pre><font face = "Tohoma" size = 4 color = "indigo"><b> 
Hi,
9(x+1)^2+25(y-2)^2=225
{{{(x+1)^2/25 +(y-2)^2/9 = 1}}}
 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.
center: (-1,2)
Foci: {{{sqrt(25-9)}}} = 4  Foci (-4,2) and ( 2,2)
length of major axis = 10  (a = 5)  
Length of minor axis = 6   (b = 3)
{{{drawing(300,300,   -10,10,-10,10,  arc(-1,2,10,6),
 grid(1),
circle(-1, 2,0.4),
circle(-4, 2,0.4),
circle(2, 2,0.4),
graph( 300, 300, -10,10,-10,10))}}}

8x^2+2y^2=32
{{{x^2/4 + y^2/16 = 1}}} C(0,0) major axis = 8 and minor = 4
foci are (0, ± sqrt(12))  sqrt(16-4)