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.