Circle Graph

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

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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.
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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.
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circle graph

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