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Formulas for the Standard and General Equation of a Circle



Posted: May 29th, 2015  
If the equation of the circle includes (h,k) then it is the Standard Equation of the Circle. Another characteristic of the standard equation of the circle that you can use to identify it is how closely related it is to the distance formula. For example, the standard equation of the circle and the distance formula are the same if you change "d" for distance to "r" for radius and square both sides of the distance formula. While in the distance formula "h" and "k" would be written as "x1" and "y1", in the standard equation of the circle "h" and "k" are the x and y coordinate which is the center of the circle.
In the formula for the General Equation of the Circle, the coefficient A is the same for x & y because it must be the same. You can find the Standard Equation of the Circle if you have the General Equation of the Circle. The Standard Equation of the Circle does not include the coordinates for the center of the circle (h,k) however (h,k), can be found from the Standard Equation of the Circle by a technique called completing the square. It appears that the General Equation of the Circle does not include the radius (r), however the constant D will go through some changes while completing the square and turn into the radius of the General Equation of the Circle.
by Andrea Boggs


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