Drawing Ellipse on the Site.
What is Ellipse:
(From: https://www.mathsisfun.com/geometry/ellipse.html )
Ellipse is a squash circle having two Major Axis and Minor Axis with two focus points called foci points.
The distance from F to P to G is always the same value. So we can say An ellipse is the set of all points on a plane whose distance from two fixed points F and G add up to a constant.
In other words, when we go from point "F" to any point on the ellipse and then go on to point "G", we always travel the same distance.
You Can Draw It Yourself
Put two pins in a board, put a loop of string around them, and insert a pencil into the loop. Keep the string stretched so it forms a triangle, and draw a curve ... you will draw an ellipse.
Major and Minor Axes
The Major Axis is the longest diameter. It goes from one side of the ellipse, through the center, to the other side, at the widest part of the ellipse. And the Minor Axis is the shortest diameter (at the narrowest part of the ellipse).
The Semi-major Axis is half of the Major Axis, and the Semi-minor Axis is half of the Minor Axis.
The area of an ellipse is:
π × a × b
where a is the length of the Semi-major Axis, and b is the length of the Semi-minor Axis.
Be careful: a and b are from the center outwards (not all the way across).
(Note: for a circle, a and b are equal to the radius, and you get π × r × r = πr2, which is right!
Perimeter of Ellipse is Very Difficult to calculate.
But a simple approximation that is within about 5% of the true value (so long as a is not more than 3 times longer than b) is as follows:
How to find the Foci Points of Ellipse:
Each ellipse has two foci (plural of focus) as shown in the picture here:
As you can see, c is the distance from the center to a focus.
We can find the value of c by using the formula
c2 = a2 - b2.
Notice that this formula has a negative sign, not a positive sign like the formula for a hyperbola.
We can easily find c by substituting in a and b and solving. That, in turn, gives us the location of our foci.
This shows how to find the two foci of an ellipse given its width and height (major and minor axes). This can be used to find the two focus points when you are planning to draw an ellipse using the string and pins method. Uses a compass, no measuring is used. A Euclidean construction.
1. With the compasses' point on the center, set the compasses' width to half the width (major axis) of the ellipse.
2. Move the compasses' point to one end of the minor axis of the ellipse and draw two arcs across the major axis.
3. Where these arcs cross the major axis are the foci of the ellipse. Label them F1, F2.