You can construct a conic section on any plane by defining a fixed point called the focus (F), a moving point (P) and a straight line called a directrix D!
The locus of P will describe a conic section as long as the ratio of the distance PF (from the point P to the focus F) and the distance PD (perpendicular distance from the point P to the directrix D) is a constant, called the eccentricity (e = PF/PD).
The sections constructed from the locus depending on the value of e are:
- Ellipse (0 < e < 1)
- Parabola (e = 1)
- Hyperbola (e > 1)
In this video, I show you an exercise that you can do at home to help you construct a conic section with conic graph paper!
To understand more about locus, please take a look at this page: Locus in the Cartesian Plane - Part 1
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