# Circle Graph

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

In this section we will discuss circle graph with center as origin and center other than origin.
A circle is the set of all points in a plane which are at a constant distance from a fixed point in the plane. A fixed point is called the 'center' and the constant distance is called the radius of the circle.
A circle has an eccentricity of zero, so the eccentricity shows you how "un-circular" the curve is. Bigger eccentricities are less curved. The standard equation of circle with center as origin (0,0)is given by
x2 + y2 = r2

Examples on circle graph
The equation of circle is x2 + y2 = 42 where radius is 2. So the graph will look like : The standard equation of circle with center as (h,k) is given by
(x - h)2 + (y - k)2 = r2 where h and k are the center of the circle.
Example :

(x - 2)2 + (y - 1)2 = 52
Here the center of the circle is (2,1) and radius is 5.So the graph will be Examples
1) Find the equation of the circle with center(-3,2) and radius 5.
Solution :
Here, the center (h,k) is (-3,2) and radius is 5. Hence, substituting, h= -3 and k = 2 and r = 5 in
(x - h)2 + (y - k)2 = r2
[x-(-3)]2 + (y - 2)2= 52
⇒ (x+3)2 + (y-2)2= 25.
_________________________________________________________________
2) Find the center and radius of the circle. x2 + y2 -2x + 4y = 8
Solution :
The given equation is (x2 -2x)+ y2 + 4y ) = 8
Now, completing the square within the parenthesis, we get
(x2- 2x + 1) +(y2 +4y + 4) = 8 + 1 + 4
(x -1)2 + (y + 2)2 = (√13)2
Comparing it with the equation of the circle, we see that the center of the circle is (1,-2) and radius is √13.
_________________________________________________________________

circle graph

Graph Dictionary