Circle : Equation of Circle , Equation of Circle in different cases , Position of a Point with respect to circle.

Equation of Circle

 

Let C(i, j) be the centre of the circle and CP(r) be the radius of the Circle, then the equation of the circle is 

Circle equation

Now, origin (0, 0) be the centre of the circle then equation 1 becomes,

The area of the circle is given by

General Equation of Circle

The General equation of the second degree may represent a circle if the coeffcient of and coeffcient of are identical and coeffcient of xy becomes zero i.e

    

represents a circle if a =b i.e 

then equation 1 reduces as 

whose centre and radius are 

Equation of circle in diameter form

Let 

be the end points of a diameter of the given circle and let P(x,y) be any point on the circle such that

Slope of AP

for a perpendicular,  m1 * m2 = 1 i.e AP * BP = -1

Equation of Circle in different cases

Case 1:

Circle equation

When circle passes through origin (0,0). let the equation of the circle be

it passes through origin (0,0)

equation 1 becomes

 

Case 2:

When circle passes through x- axis. let the centre of the circle be C(i, j) and toches x-axis at point P , then radius of the circle is 

equation of the circle 

 

Case 3:

When circle passes through y- axis. let the centre of the circle be C(i, j) and toches y-axis at point P , then radius of the circle is 

equation of the circle 

Case 4:

When circle toches both axis. In this case

then equation of the circle 

 

Post By : Rahul Kumar 29 Jan, 2020 2507 views Maths