Lesson Basic formulas in a circle

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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. d=2%2Ar

Circumference of the 'Circle':
Perimeter(circumference) of the circle is given by the formula.
P=2%2Api%2Ar
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.
A=+pi%2Ar%5E2
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

%28x-a%29%5E2%2B%28y-b%29%5E2=r%5E2

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

In "Parametric form", the equation of the same circle is written as:
x=a%2Br%2ASin%28t%29
y=b%2Br%2ACos%28t%29
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 "-infinity to +infinity".

Solution of this equation gives the set of all points (x,y) 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 (r%5Bo%5D, rho) and radius "R" is

r%5E2-2%2Ar%2Aro%2ACos%28theta+-+rho%29%2B%28ro%29%5E2=R%5E2

Solution of this equation gives the set of all points (r,theta) which are at constant distance
'R' from a fixed point (r%5Bo%5D, rho).

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

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