1. ## ellipse

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

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

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

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

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

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

Does this make sense?

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