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Notice that the general equation of an ellipse does not easily tell us what a certain ellipse looks like.

On the other hand, the standard equation of an ellipse provides information about the centre coordinates and lengths of the horizontal and vertical axes.

Recall that this was also true of the general and standard equations of a circle.

When asked to describe the picture of a circle given its general equation, we rewrote the general equation into standard form using a method called completing the square.

We use this same method when rewriting the equation of an ellipse from general to standard form.

Let's look at a few examples.