SOLUTION: determine the equation of the curve such that the sum of the distance of any point on the curve from two points whose coordinate are (-3,0) and (3,0) is always equal to 8

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: determine the equation of the curve such that the sum of the distance of any point on the curve from two points whose coordinate are (-3,0) and (3,0) is always equal to 8      Log On


   

Question 1086399: determine the equation of the curve such that the sum of the distance of any point on the curve from two points whose coordinate are (-3,0) and (3,0) is always equal to 8
Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
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Ellipse with foci at the points (-3,0) and (3,0) and the major axis of 8 units long.


Hence, the major semi-axis is 4 units long.


Then the minor semi-axis is sqrt%284%5E2+-+3%5E2%29 = sqrt%287%29.


The equation of the ellipse is


x%5E2%2F16 + y%5E2%2F7 = 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".