The question is: Sketch 4x^2 + y^2 - 2y = 8 on a clearly labelled diagram, making clear the main relevant features of the graph.

Can I manipulate it such that it has an equation of an ellipse i.e. x^2/(3/2)^2 + (y-1)^2/3^2 = 1 ?

Or should I just make y the subject i.e. y = 1 +or- sq root (9-4x^2) then sketch using my GC?

Both give different sketches so which is the correct method or is there another way to do this question?