Suppose A,B,C,D are points on an ellipse such that the segments AB and CD intersects at a focus F. Given that AF=3, CF=4, and BF=5, what is DF?

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brentkenneth0618

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Suppose A,B,C,D are points on an ellipse such that the segments AB and CD intersects at a focus F. Given that AF=3, CF=4, and BF=5, what is DF?
 
brentkenneth0618 said:
Suppose A,B,C,D are points on an ellipse such that the segments AB and CD intersects at a focus F. Given that AF=3, CF=4, and BF=5, what is DF?
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Did you draw an approximate sketch of the ellipse and points F, A, B, C & D? ................[edited]

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
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Subhotosh Khan said:
Did draw an approximate sketch of the ellipse and points F, A, B, C & D?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
Click to expand...
None sir. There is no indicated illustration on our worksheet. Just the points and the corresponding values of segments.
 
brentkenneth0618 said:
None sir. There is no indicated illustration on our worksheet. Just the points and the corresponding values of segments.
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I am suggesting that YOU sketch the ellipse and the points on the ellipse - as a start of the "solution process".
 
brentkenneth0618 said:
Suppose A,B,C,D are points on an ellipse such that the segments AB and CD intersects at a focus F. Given that AF=3, CF=4, and BF=5, what is DF?
Click to expand...
I can't think of any properties of an ellipse that would help in this. However, in playing with a picture, I found that there are many configurations that work, which all give the same solution, as the problem implies. Here is one:

1605840359731.png

Can you tell us anything about the context that might suggest ideas? If this is for a class, what have you learned about ellipses?

But after browsing Wikipedia, it occurred to me that this might be relevant: https://en.wikipedia.org/wiki/Ellipse#Polar_form_relative_to_focus

If you've learned that (or can learn it now), you can solve the problem! It's beautiful.
 
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