The ellipse is the type of conic section formed by the locus of a moving point P, such that the ratio (eccentricity) of its distance to a fixed focal point F, to a fixed imaginary line called the directrix D is a positive constant that is less than 1.
Try this experiment at home to better understand how mathematically, an ellipse is formed. You'll need 2 thumb tacks, string, paper and a pencil or a pen.
1. Secure the thumb tacks so that the distance between them is less than the length of the string.
2. Tie the string around both tacks
3. Pull the string taut with the pencil
4. Keeping the string taut, mark out the shape you get as you move the pencil around.
You should end up with an ellipse! And this is mathematically how we derive the standard form of the equation of the ellipse.
We simply require the distance formula for PF (the distance from point P to the positive focus) and PF' (the distance from the point P to the negative focus).
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