Question 141095
4x^2+y^2+8x-4y-28=0 


Sort it out and factor the coefficient of x^2.  Leave spaces in order to complete the square in the next steps:

{{{4x^2 +8x +_____+y^2 -4y + _____ = 28}}}

{{{4(x^2 +2x +_____)+y^2 -4y + _____ = 28 + _____ + _____}}}


To complete the square, you must take half of the x coefficient (Half of 2 is 1, and square which is 1.  On the right side, however, you must add 4*1 which is 4.  It should look like this: 

{{{4(x^2 +2x +_____)+y^2 -4y + _____ = 28 + _____ + _____}}}
{{{4(x^2 +2x +1  )+y^2 -4y + 4 = 28 + 4*1 + 4}}}

{{{4(x+1)^2 + (y-2)^2 = 36 }}}


Divide both sides by 36 to write this in standard form for an ellipse:

{{{4(x+1)^2 + (y-2)^2 = 36 }}}
{{{(4(x+1)^2)/36 + ((y-2)^2)/36 = 36/36 }}}
{{{((x+1)^2)/9 + ((y-2)^2)/36 = 1 }}}


This is an ellipse, with center at (-1,2), with a "radius" of 3 in the x direction, and a "radius" of 6 in the y direction.


R^2