Have you ever seen a circle? This two-dimensional shape is in a clock, base of a glass, and a coin. A circle is a set of points on a particular plane with same, fixed distance from its center. In mathematics, there are some familiar circle terms, such as radius (radii), diameter, and circumference. You probably will need math help about circle formulas and equations for your homework. Don’t worry, you can learn more and understand about circle formulas and equations in the following passages.
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Radius or radii (r) is the distance from the center to a point of the circle. Radius always the same value for all points. Diameter (d) is the distance from a point to another point through the center. Its value is twice of radius. Circumference is the distance around your circle.
How do we calculate area and circumference of a circle?
A = πr^{2} = π ( d/2 )^{2}
C = πd = 2πr
The symbol π (pi) is a Greek letter with value of 3.14 (rounded). It is a magical number which has to be remembered every time you deal with circle.
r = 20 cm
A = πr^{2} = π x 20^{2} = 3.14 x 400 = 1,256 cm^{2}
C = 2πr = 2 x 3.14 x 20 = 125.6 cm
Imagine a sector as a slice of pizza, a part of a big circle.
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A = πr^{2} ( n/360 )
With n is the sector angle.
There are two forms of circle equations:
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(x – a)^{2} + (y – b)^{2} = r^{2}
(x, y) is your point and (a, b) is the center.
General form is an extended version of standard form.
x^{2} + y^{2} + Ax + By + C = 0
A, B, and C are constants.
Examples:
Find the circle equation!
1.
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(a, b) = (1, 0)
r = 1
Solution:
(x – a)^{2} + (y – b)^{2} = r^{2}
(x – 1)^{2} + (y – 0)^{2} = 1^{2} (standard form)
(x^{2} – 2x + 1) + y^{2} = 1
x^{2} + y^{2} – 2x = 0 (general form)
2.
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(a, b) = (3, 1)
r = 2
Solution:
(x – a)^{2} + (y – b)^{2} = r^{2}
(x – 3)^{2} + (y – 1)^{2} = 2^{2}
(x – 3)^{2} + (y – 1)^{2} = 4 (standard form)
(x^{2} – 6x + 9) + (y^{2} – 2y + 1) = 4
x^{2} + y^{2} – 6x – 2y + 9 + 1 = 4
x^{2} + y^{2} – 6x – 2y + 6 = 0 (general form)
You can use these circle formulas and equations when do your homework, calculate area or circumference of a circular land or fence, even make a craftwork! They can be applied to almost all things related to circle or circular objects.
1. https://www.mathsisfun.com/algebra/circle-equations.html
You can read about standard and general forms of circle equation with simple illustrations. This web also shows you how to plot a circle.
2. http://www.wikihow.com/Calculate-the-Area-of-a-Circle
To know how to calculate the area of circle using various ways, you may find this site useful. Real examples are also given using real objects.
3. http://www.wikihow.com/Work-out-the-Circumference-of-a-Circle
This webpage contains various methods to find circumference. Accompanied with clear illustrations, it will guide you step by step.
4. http://www.mathwarehouse.com/geometry/circle/equation-of-a-circle.php
Here, you’ll learn about the definition of a circle and the circle equation. Examples of the problems are given along with the solutions.
5. http://math.com/school/subject3/lessons/S3U1L6GL.html
This math web brings you the definition of circle, radius, chord, diameter, arc, and semicircle. In-depth learning about angle is also available.
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