Question 920593
 x^2+4y^2+4x-8y-8 = 0
(x-2)^2-4  + 4(y-1)^2 -4   -8 = 0
(x-2)^2  + 4(y-1)^2 = 16
(x-2)^2/16  + (y-1)^2/4 = 1  Ellipse C(2,1) major axis along y = 1
 Standard Form of an Equation of an Ellipse is {{{(x-h)^2/a^2 + (y-k)^2/b^2 = 1 }}} 
{{{(x-2)^2/4^2 + (y-2)^2/2^2 = 1 }}} 

{{{drawing(300,300,   -6, 6, -6, 6, grid(1), arc(2,1,8,4),
 circle(2, 1,0.2),
graph( 300, 300, -6, 6, -6, 6,0,1 ))}}}