Precalculus Examples
Find the Circle Using the Diameter End Points (-3,8) , (7,6)
Step 1
The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circumference of the circle. The given end points of the diameter are and . The center point of the circle is the center of the diameter, which is the midpoint between and . In this case the midpoint is .
Use the midpoint formula to find the midpoint of the line segment.
Substitute in the values for and .
Cancel the common factor of and .
Cancel the common factors.
Cancel the common factor.
Step 2
Find the radius for the circle. The radius is any line segment from the center of the circle to any point on its circumference. In this case, is the distance between and .
Use the distance formula to determine the distance between the two points.
Substitute the actual values of the points into the distance formula.
Step 3
is the equation form for a circle with radius and as the center point. In this case, and the center point is . The equation for the circle is .
Algebra Examples
Find the Center and Radius x^2+y^2=7
Step 1
This is the form of a circle. Use this form to determine the center and radius of the circle.
Step 2
Match the values in this circle to those of the standard form. The variable represents the radius of the circle, represents the x-offset from the origin, and represents the y-offset from origin.
Step 3
The center of the circle is found at .
Center:
Step 4
These values represent the important values for graphing and analyzing a circle.
Center:
Radius:
Please provide any value below to calculate the remaining values of a circle.
While a circle, symbolically, represents many different things to many different groups of people including concepts such as eternity, timelessness, and totality, a circle by definition is a simple closed shape. It is a set of all points in a plane that are equidistant from a given point, called the center. It can also be defined as a curve traced by a point where the distance from a given point remains constant as the point moves. The distance between any point of a circle and the center of a circle is called its radius, while the diameter of a circle is defined as the largest distance between any two points on a circle. Essentially, the diameter is twice the radius, as the largest distance between two points on a circle has to be a line segment through the center of a circle. The circumference of a circle can be defined as the distance around the circle, or the length of a circuit along the circle. All of these values are related through the mathematical constant π, or pi, which is the ratio of a circle's circumference to its diameter, and is approximately 3.14159. π is an irrational number meaning that it cannot be expressed exactly as a fraction (though it is often approximated as 22/7) and its decimal representation never ends or has a permanent repeating pattern. It is also a transcendental number, meaning that it is not the root of any non-zero, polynomial that has rational coefficients. Interestingly, the proof by Ferdinand von Lindemann in 1880 that π is transcendental finally put an end to the millennia-old quest that began with ancient geometers of "squaring the circle." This involved attempting to construct a square with the same area as a given circle within a finite number of steps, only using a compass and straightedge. While it is now known that this is impossible, and imagining the ardent efforts of flustered ancient geometers attempting the impossible by candlelight might evoke a ludicrous image, it is important to remember that it is thanks to people like these that so many mathematical concepts are well defined today.
Circle Formulas
D = 2R C = 2πR A = πR2 | where: R: Radius | |