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Circle GraphCovid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! 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 "uncircular" the curve is. Bigger eccentricities are less curved. The standard equation of circle with center as origin (0,0)is given by x^{2} + y^{2} = r^{2} Examples on circle graph The equation of circle is x ^{2} + y ^{2} = 4 ^{2} 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} = r^{2} where h and k are the center of the circle. Example : (x  2)^{2} + (y  1)^{2} = 5^{2} 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} = r ^{2} [x(3)] ^{2} + (y  2) ^{2} = 5 ^{2} ⇒ (x+3) ^{2} + (y2) ^{2} = 25. _________________________________________________________________ 2) Find the center and radius of the circle. x ^{2} + y ^{2} 2x + 4y = 8 Solution : The given equation is (x ^{2} 2x)+ y ^{2} + 4y ) = 8 Now, completing the square within the parenthesis, we get (x ^{2}  2x + 1) +(y ^{2} +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 Home Page Covid19 has affected physical interactions between people. Don't let it affect your learning.
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