Lesson Basic formulas in a circle

In this lesson we will be looking at the definition, different equations, area and circumference of the circle.

Circle
A circle is the set of all point in a plane that are at constant distance from a fixed point.
Fixed point is called the "center of the circle" and the constant distance is called the
" radius of the circle".



In the figure above,
C is the center of the circle.
r is the radius of the circle.
d is the diameter of the circle. It is twice of the radius.

Circumference of the 'Circle':
Perimeter(circumference) of the circle is given by the formula.

Where:
P is the circumference of the circle.
r is the radius of the circle.


Area of the 'Circle'
Area of the circle is given by the formula.

Where:
A is the area of the circle.
r is the radius of the circle.


Equation of the 'Circle'

In "x-y coordinate system" ('Cartesian coordinates'), The equation of the circle with center
(a,b) and radius 'r' is



Solution of this equation gives the set of all points (,) which are at constant distance
'r' from a fixed point (a,b).

In "Parametric form", the equation of the same circle is written as:


Where:
(a,b) is the center of the circle.
'r' is the radius of the circle.
't' is the parameter which can take any real value between " to +".

Solution of this equation gives the set of all points (,) which are at constant distance
'r' from a fixed point (a,b).

In "Polar coordinate system", the equation of the same circle is written as:
The general equation for a circle with a center at (, ) and radius "R" is



Solution of this equation gives the set of all points (r,) which are at constant distance
'R' from a fixed point (, ).

For further reading
on Circle refer to Wikipedia
on different Coordinate systems refer to Lesson