SOLUTION: Find the general equation of the ellipse whose major axis is 20 units and the foci are the points of coordinates (0, 5√3) and (0, −5√3).

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the general equation of the ellipse whose major axis is 20 units and the foci are the points of coordinates (0, 5√3) and (0, −5√3).      Log On


   

Question 1193860: Find the general equation of the ellipse whose major axis is 20 units and the foci are
the points of coordinates (0, 5√3) and (0, −5√3).
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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Find the general equation of the ellipse whose major axis is 20 units and the foci are
the points of coordinates (0, 5√3) and (0, −5√3).
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From the post, the ellips has the center at point (0,0), which is the origin of the coordinaste system.

Foci are located at y-axis.


It means that the major axis lies on vertical y-axis.


The major axis is 20 units long; hence, the major semi-axis is a = 10 units long.


The eccentricity (the distance from the center to each foci) is  c = 5%2Asqrt%283%29.


It means that the minor semi-axis is  

    b = sqrt%28a%5E2+-+c%5E2%29 = sqrt%28100-%285%2Asqrt%283%29%29%5E2%29 = sqrt%28100-25%2A3%29 = sqrt%2825%29 = 5.


Now the general equation of the ellipse is

    y%5E2%2F10%5E2 + x%5E2%2F5%5E2 = 1.    ANSWER

Solved.

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To understand in full what is written in the post,  see the lesson
    - Ellipse definition, canonical equation, characteristic points and elements
in this site.