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talk about taking the equation of an ellipse that is written in general form and transforming it into the very useful standard form so that you could find its graph so let me remind you that in general form any the equation of an ellipse could look like this with a and C having the same sign if they had different signs we would be talking about a hyperbola but for it to be an ellipse the equation would look something like this with these two having the same sign and when we write it in standard form notice we have these nice perfect squares in the numerator the center is HK in both of these cases and if you look at it they at first glance these look the same but notice here on the left the a squared is in the denominator of our first term and here the a squared is in the denominator of the second one and thats because the a squared is always the larger of the two denominators when were talking about an ellipse so it may be underneath the x squared or it may be underneath the Y square