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.
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ellipse
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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
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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!
\(\displaystyle \text{Plot the foci and we see that the center is at }(2,5)\text{, and }c = 4.\)
\(\displaystyle \text{The equation has the form: }\:\frac{(x-2)^2}{a^2} + \frac{(y-5)^2}{b^2} \:=\:1\)
\(\displaystyle \text{"The sum of the distances is 10": }\:a \,=\, 5\)
\(\displaystyle \text{From }a^2\:=\:b^2+c^2\text{, we have: }\:5^2\:=\:b^2 + 4^2 \quad\Rightarrow\quad b^2 \,=\,9\)
\(\displaystyle \text{Therefore, the equation is: }\;\frac{(x-2)^2}{25} + \frac{(y-5)^2}{9} \;=\;1\)
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.
\(\displaystyle \text{Plot the foci and we see that the center is at }(2,5)\text{, and }c = 4.\)
\(\displaystyle \text{The equation has the form: }\:\frac{(x-2)^2}{a^2} + \frac{(y-5)^2}{b^2} \:=\:1\)
\(\displaystyle \text{"The sum of the distances is 10": }\:a \,=\, 5\)
\(\displaystyle \text{From }a^2\:=\:b^2+c^2\text{, we have: }\:5^2\:=\:b^2 + 4^2 \quad\Rightarrow\quad b^2 \,=\,9\)
\(\displaystyle \text{Therefore, the equation is: }\;\frac{(x-2)^2}{25} + \frac{(y-5)^2}{9} \;=\;1\)