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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 = .
It means that the minor semi-axis is
b = = = = = 5.
Now the general equation of the ellipse is
+ = 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.