You can put this solution on YOUR website! Change from general to standard form
4x^2 + y^2 - 8x - 2y + 1 = 0
4x^2 - 8x + y^2 - 2y + 1 = 0
complete the square:
4(x^2-2x+1)+(y^2-2y+1) =-1+4+1
4(x-1)^2+(y-1)^2=4
This is an equation of an ellipse with vertical major axis and center at (1,1)