What is a locus?
A locus is simply a fancy word for "set of points". The plural form is "loci", just like the plural of "radius" is "radii" and that of "focus" is"foci". For example, a circle with its center at the point (h, k) can be defined as the locus of all points that are equidistant from the point (h, k).
What is a conic section?
Hundreds of years ago, the ancient Greeks had a lot of spare time, so they thought about the different ways in which a cone can be sliced. (They also thought about whether the Earth is round or flat, why the sky is blue, and why objects float or sink.) The different shapes that are formed when a plane cuts a cone are called conic sections.
There are many uses for conic sections in the real world. The satellite receiver that brings you your favorite TV shows is probably a parabolic antenna. Bridges can be built in the shape of parabolas or hyperbolas. The planets move around the Sun in elliptical orbits. When you throw a basketball, it travels in a path defined by a parabola. Ellipses, circles, parabolas, and hyperbolas are all conic sections.
The Circle
As we learned earlier, a circle is the locus of points that are equidistant from a fixed point called the center.

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