The key to this is to factor out in such a way in order to form the standard equation of an ellipse. To do this, we complete the square. With the 4x^2 + 4x, you know that you need to add 16 in order to make it a square, so take out the 16 from the 541. You will get 4(x + 2)^2 + 25y^2 + 250y + 525 = 0. Do the same thing with the y, and you get 4(x + 2)^2 + 25(y + 5)^2 = 100. Divide both sides by 100 and you will get an ellipse. Just remember to complete the square with both x and y, and you will be fine. THis will in the end make an ellipse.