SOLUTION: Find an equation of the set of points in a plane such that the sum of distances between each point of the set and the points (1,0) and (-1,0) is 8 units

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Question 1033012: Find an equation of the set of points in a plane such that the sum of distances between each point of the set and the points (1,0) and (-1,0) is 8 units
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
The description of an ellipse with foci (1,0) and (-1,0).

, using Distance Formula. Simplify the equation. Adjust into Standard Form.
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
Find an equation of the set of points in a plane such that the sum of distances between each point
of the set and the points (1,0) and (-1,0) is 8 units.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

It is an ellipse, and it is its characteristic property.


Read about it in the lesson Ellipse focal property in this site.

The foci of this ellipse are the points (1,0) and (-1,0). 

The major semi-axes of the ellipse a =  = 4 is half of the sum of these distances. 

The minor semi-axes b =  =  = , according to that lesson.

So, the ellipse canonical equation is 

 = ,   or

 = .


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