Question 416830
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Hi
4X^2 + Y^2 - 4Y - 32 = 0
4X^2 + (Y-2)^2 - 4 - 32 = 0
4X^2 + (Y-2)^2 = 36
 (Y-2)^2/36 + X^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 units the respective distances from
 center right/left and up/down for the vertices
{{{drawing(300,300,     -10, 10, -10, 10,    arc(0,2,6,12),
 grid(1),
circle(0,2,0.4),
circle(0,8,0.4),
circle(0,-4,0.4),
circle(3,2,0.4),
circle(-3,2,0.4),

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