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# Super Hard Ellipse Problem Help Plz!

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I've literally tried to approach this problem so many ways but still can't seem to solve it.

The graph of an equation $$\sqrt{(x-3)^2 + (y+4)^2} + \sqrt{(x+5)^2 + (y-8)^2} = 20$$ is an ellipse. What is the distance between its foci?

Mar 18, 2020

#1
+23553
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I am not sure of this answer:

An ellipse is a graph of points where the sum of the distances from two foci is a constant....

this looks like the equation for two distances from two foci

first foci  would be 3 , -4        other is   -5, 8

distance between these points is      (3- -5)^2  +  (-4 - 8)^2 = d^2

64       + 144   = d^2                      d = sqrt 208

Mar 18, 2020
#3
+1

Oh thank you so much! Thank you for helping me see the problem from different perspective and helping me solve it out, I really appreciate it!!! I've been stuck on this problem for days and I'm so happy I finally managed to get past it. Thank you!

Guest Mar 18, 2020
#2
+111360
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I believe  that  EP's answer is correct   !!!!

Here's a graph  :  https://www.desmos.com/calculator/m73xbuxuph

Note  that  the  center  of  this  ellipse  is  the  midpoint   between  (-5,8) and (  3, - 4)

Thus.....the center  is    ( -1, 2)

Mar 18, 2020