SOLUTION: In ellipse situation, find the equation of the locus of a point which moves so that the summation of its distance from (-2,2) and (1,2) is 5.

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Question 1082536: In ellipse situation, find the equation of the locus of a point which moves so that the summation of its distance from (-2,2) and (1,2) is 5.
Answer by ikleyn(52817) About Me  (Show Source):
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The figure is an ellipse     ("the locus of a point which moves so that the summation of its distance from two given points is constant").


The major axis is the line y = 2 parallel to x-axis.


The major semi-axis length is half of that distance of 5 units, i.e. a= 2.5 units.


The distance between foci is 1 - (-2) = 3.
So, the linear eccentricity is half of that, i.e. c= 1.5.


Find the minor semi-axis length "b" from the equation c%5E2 = a%5E2+-+b%5E2:

b = sqrt%282.5%5E2-1.5%5E2%29 = 2.


Now the equation of the ellipse is 

x%5E2%2F2.5%5E2 + y%5E2%2F2%5E2 = 1.

See the lesson
    - Ellipse definition, canonical equation, characteristic points and elements
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic
"Conic sections: Ellipses. Definition, major elements and properties. Solved problems".