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Favorite Answer
Physically :
If you have a loop of string and two nails at the focii, you can quickly sketch an ellipse
Algebraically
You need the semi major axis, a , and the semi minor axis , b, and a form of the ellipse to calculate some in between points :
so
If x^2 /a^2 + y^2 /b^2 = 1
a and b are needed for the intercepts
and y = ± b/a√(a^2-x^2) will give in between points.
If our ellipse was x^2/36 +y^2/25 = 1
then we get the four points ( 6,0) (-6,0) ( 0,5) and ( 0,-5) from a^2 = 36 and b^2 =25
Then use y = ±(5/6)√(36-x^2) and a calculator to get points between 0 and 6
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Once you have enough points in Quadrant I , you can copy all those points via reflection to the other three quadrants , and draw a smooth curve thru all the points .
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Draw a circle first for the skeleton
Then stretch the radius (equally distance though) as much as you like
Anonymous
if you have a ti-84 and higher it can do it