Overview:
The circle is the conic section that is formed when a plane is perpendicular to the axis of a cone, so the circle cuts through it evenly. It is one of the simplest of all the geometric forms.
What Is a Circle?
The circumference of a circle is defined as the points in a plane that are a given distance from a fixed central point. The radius is the line segment from the center of the circle to a point on the circumference. It is the same length from the center of the circle to any point on the circumference of the circle. The length of the circumference equals the familiar formula 2πr, where the radius is r and the constant π is equal to 3.1417, and is the best known of the irrational numbers.
What Is the Area of a Circle?
The area of a circle can be described by the equation πr2, where r is the radius. When all the points in the circle are included, it is also known as the area of a disk. The equation A = πr2 is also a common example of a second-degree closed equation.
What Is the Distance Formula?
The formula for finding the distance between the endpoints of any line segment in a two-dimensional plane is given by the equation √[(x1-x2)2 + (y1-y2)2] where the point at one end of the line segment has the coordinates x1, y1 and the point at the other end of the line segment has the coordinates x2, y2. For example, suppose Point 1 has the coordinates (0, -1) and Point 2 has the coordinates (4, -1). In that case, (0-4) will be -4 and (-1 + 1) will be 0. The square root of 16 – 0 is 4, so the line segment is 4 units long.
What Is the Distance Formula for a Circle?
Using the distance formula, the center and radius of any circle can be found in the two-dimensional plane. The difference is that the general form of the equation will have negative signs. If the center of a circle is at the origin point of a graph, the coordinates for the radius will follow a specific pattern x2 + y2 = r2. Suppose that the coordinates of the circle follow the equation x2+ y2 = 16. The radius will be √16, or 4 units long.
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