Fun with coordinate system

Ellipse

foci: Imagine a fat ellipse, every ellipse has two foci, take there distance to a point P on the ellipse. because it’s a foci the addition of these distances will be constant (that’s how we define a foci, we will later talk about how to find them and why are they unique)

What about hyperbola

Imaging hyperbolas as ellipses whose left part is moved to the right and right part moved to the left

Parabola

pick a point (any point, it will be our focus. so, focus ) and a straight line (in any direction). parabola is the locus of all the point, which is the same distance from the line and that point

Line

section formula

Finding Magic.

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