ellipse

**dan123** · May 31st 2009, 04:34 PM

an ellipse has the following points

(-2,3) left
(2,5) top
(6,3) right
(2,1) bottom

write the equation in general and standard form of the ellipse

**Chris L T521** · May 31st 2009, 05:09 PM

Originally Posted by dan123

an ellipse has the following points

(-2,3) left
(2,5) top
(6,3) right
(2,1) bottom

write the equation in general and standard form of the ellipse

The length of the axis are as follows:

Between $\left(-2,3\right),\left(6,3\right)$ : length is 6-(-2)=8
Between $\left(2,5\right),\left(2,1\right)$ : length is 5-1=4

So it follows that the major axis is parallel to the x axis and $a=4$ , and the minor axis is parallel to the y axis and $b=2$ .

The ellipse will take the form $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ .

I leave it for you to verify that the center of the ellipse is (2,3).

Therefore, the equation of the ellipse is $\frac{(x-2)^2}{16}+\frac{(y-3)^2}{4}=1$

Does this make sense?

**dan123** · May 31st 2009, 05:52 PM

yeah,it does,I knew the formulas and everything,but I just find it difficult to put it all together

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