Just like polynomials, there are different forms for the equation of the graph of ellipse. The general form, which was mentioned before is Ax2 + By2 + Cx + Dy + E = 0. The advantage of this for is that it is a general for all graphs in conics, while the disadvantage is that this form tells us little of the graph of the equation.
The second form, which is what we’ll usually use, is the standard form. The standard form of the equation for an ellipse is：
[(x-h)/a)2] + [(y-k)/b]2 = 1In this form, we can pretty much tell what the graph of this equation will be once we understand what each component of it stands for.
If you are familiar with function translation and transformation, you should realize this equation is just a transform/translated version of the equation of a unit circle.
The equation for a unit circle with centre (0, 0) is x2+y2=1. From a translation/transformation point of view, we are just stretching the unit circle by a factor of a horizontally, and by b vertically. We are then, translating the resulting graph, h units horizontally and k units vertically.
Since the centre of the unit circle is just (0, 0) and a radius of 1, we can easily infer its new centre as well as horizontal and vertical radii. So in short, we have the graph of the ellipse centred at (h, k) and with horizontal radius a, vertical radius b. That being said, if you can put an equation of ellipse/circle in the standard form, then you can obtain the graph of the ellipse very easily.
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This article was written for you by Brian, one of the tutors with SchoolTutoring Academy.