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.

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(52858) (Show Source): You can put this solution on YOUR website!
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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  = :

b =  = 2.


Now the equation of the ellipse is 

 +  = 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".

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