ellipse

chelsearenee

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An ellipse has a foci (-2,5) and (6,5). The sum of the distance from each point of the ellipse to the foci is 10. Find the equation of the ellipse.
 
chelsearenee said:
An ellipse has a foci (-2,5) and (6,5). The sum of the distance from each point of the ellipse to the foci is 10. Find the equation of the ellipse.


To start - go to google.com

type in

definition of ellipse equation

You'll find 2,060,000 sites ready to help you with examples.

In particular go to:

http://www.maa.org/joma/Volume8/Kalman/Ellipse4.html

If you are still stuck, please write back showing us your work, indicating exactly where you are stuck - so that we know where to begin to help you.
 
Hello, chelsearenee!

An ellipse has foci (-2,5) and (6,5).
The sum of the distance from each point of the ellipse to the foci is 10.
Find the equation of the ellipse.

Plot the foci and we see that the center is at (2,5), and c=4.\displaystyle \text{Plot the foci and we see that the center is at }(2,5)\text{, and }c = 4.

The equation has the form: (x2)2a2+(y5)2b2=1\displaystyle \text{The equation has the form: }\:\frac{(x-2)^2}{a^2} + \frac{(y-5)^2}{b^2} \:=\:1

"The sum of the distances is 10": a=5\displaystyle \text{"The sum of the distances is 10": }\:a \,=\, 5

From a2=b2+c2, we have: 52=b2+42b2=9\displaystyle \text{From }a^2\:=\:b^2+c^2\text{, we have: }\:5^2\:=\:b^2 + 4^2 \quad\Rightarrow\quad b^2 \,=\,9


Therefore, the equation is:   (x2)225+(y5)29  =  1\displaystyle \text{Therefore, the equation is: }\;\frac{(x-2)^2}{25} + \frac{(y-5)^2}{9} \;=\;1

 
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