What does the graph of this equation depict? I would really like to know a step by step explanation of the graph of this equation.Thank you so much for your answer. $$4x^2+y^2-8x+2y=11$$

$$(2x-2)^2+(y+1)^2=11+4+1$$

$$\dfrac{(x-1)^2}4+\dfrac{(y+1)^2}{16}=1$$

which is an ellipse.

See this.