to check what type of conic it may be, we first check the squared variables, their coefficents and sign.
in this case 2x² and 5y² are both positive, that means we have either an ellipse or a circle.
if the coefficients are equal, boinggggg! we have a circle, or if you wish an ellipse with equal axes.
if the coefficients are different, like in this case, we have an ellipse.
