# The Circle: Definition, Conic Sections & Distance Formula

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• 0:02 A Circle
• 0:34 A Conic Section
• 1:06 The Distance Formula
• 1:57 An Example
• 2:46 Lesson Summary

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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson, and you will learn what makes a circle a conic section. Also learn how to calculate the circumference of a circle. You will learn about the one important measurement that you need for any circle.

## A Circle

What is a circle? Why are they important? A circle is a round shape whose points are all the same distance away from a center point. This kind of shape is important because we use them in our everyday lives. Think about the way we travel. It would be rather difficult if we didn't have circles (our wheels) to take us from point A to point B. Just a quick look around you and you are bound to see circles in so many different applications. You see them in cars, bicycles and even our clocks. You can't escape them!

## A Conic Section

What makes circles even more interesting in math is that they are also considered a conic section. What does this mean? This means that a circle is a shape that you get by cutting a cone. Picture an ice cream waffle cone. Now picture a knife slicing straight across. What kind of shape do you end up with? Why, a circle!

Notice how perfectly round it is:

Just like your cone has a center, our circle also has a center. When you cut a cone to get a circle, our circle's center is the same center as our cone.

## Distance Formula

The center is a very important point for our circle. It comes into play when we need to calculate the distance of our circle. In math, we call this distance around our circle, the circumference, and of course, we would have a formula for this. This formula is C = pi * d, where C stands for the circumference, pi for the mathematical constant that is approximated by 3.14, and d stands for the diameter of the circle. The diameter of our circle is the distance it takes to walk from one edge of the circle clear across the circle to the other edge, making sure that you are walking through the center of the circle. You can also calculate the diameter of the circle as twice the distance from the center of the circle to the edge.

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