How do you graph an ellipse written in general form?

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How do you graph an ellipse written in general form?

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Answer 1 · 2014-10-31T14:58:51

Graphing the general picture of an ellipse given an equation is relatively simple work. It's all about interpretation.

Let's start by looking at our standard ellipse equations:

$(x-h)^2/a^2+(y-k)^2/b^2$ (Horizontal Ellipse)

$(x-h)^2/b^2+(y-k)^2/a^2$ (Vertical Ellipse)

$a$ and $b$ simply describe the distance from the centre that the ellipse goes.

The one under $x$ is the distance it travels vertically, while the one under $y$ is the distance it travels horizontally. Do not be intimidated by the $b$ and $a$ ; they simply tell you which one is longer ( $a$ is always longer than $b$ ).

Also, $h$ and $k$ give you the coordinates for your vertex. $(h, k)$ is your vertex.

Now all you need to do is take your centre, and measure out $a$ and $b$ distance in the appropriate directions, connect the dots, and you are done. Just make sure that you square root your $a$ and $b$ before using them, and that you're using them in the right direction ( $x$ or $y$ ). Also watch out for the signs of your $h$ and $k$ .

Hope that helped :)

Answer 2 · 2014-10-31T15:27:23

It would be easiest to transform it first into standard form.

http://socratic.org/questions/how-do-i-use-completing-the-square-to-rewrite-the-equation-of-an-ellipse-in-stan#111063

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How do you graph an ellipse written in general form?

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