Definition of circle:

 Circle is the two dimensional closed geometrical figure in which the distance from the center point to the locus of all points is constant.

 

 

Domain of the circle --- all the possible x values are said to be domain of the circle.

Range of the circle----- all the possible y values are said to be range of the circle.

                                                                  

 

Standard form of circle:

 

The standard form of the circle is

                      `(x- a)^2` +`(y-b) ^2` =r2

             Here

                    r is the radius of the circle

                   (a, b) is the center of the circle.

 The formula to find the domain of circle: 

                    The domain will be {x| a-r < x < a+r}

The formula to find the range of the circle:

                  The range will be {y| b-r < y < b+r}

 

Model problems:

 

1.Find the domain and range of the circle  whose equation is x2+y2-16=0

Solution:

           Rewrite the equation to standard form.

             The standard form of the circle is

                     ` (x- a)^2` +`(y-b) ^2` =r2

                       So, x2+y2=16

                            x2+y2= 42

Here

                    r is the radius of the circle,4

                   (a, b) is the center of the circle,(0,0)

The formula to find the domain of circle: 

                   The domain will be {x| a-r < x < a+r}

                           Domain is {x|0-4 <x<0+4}

                           Domain is {x|-4<x<4}

The formula to find the range of the circle:
                   The range will be {y| b-r < y < b+r}

                           Range is {y| 0-4 <y<0+4}

                           Range is {y|-4<y<4}

                                                     

 2.find the domain and range of the circle  whose equation is (x-2)2+(y-4)2-49=0

Solution:

           Rewrite the equation to standard form.

             The standard form of the circle is

                      `(x- a)^2` +`(y-b) ^2` =r2

                       So, x2+y2=72

                            x2+y2= 72

          Here

                    r is the radius of the circle,7

                   (a, b) is the center of the circle,(2,4)

 

 

The formula to find the domain of circle: 

The domain will be {x| a-r < x < a+r}

Domain is {x|2-7 <x<2+7}

Domain is {x|-5<x<9}

The formula to find the range of the circle:
                   The range will be {y| b-r < y < b+r}

                           Range is {y| 4-7 <y<4+7}

                           Range is {y|-3<y<11}