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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.

Standard Equation of the Circle
Standard Equation of a Circle


General Equation of the Circle
General Equation 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.

Solve to find the standard equation of the circle
Example 1 of General Equation of a Circle, solve to find the standard equation of the circle.

 

step 1
Must have a coefficient of 1 for the A terms. Divide by 3 to make the A coefficient 1.
Equation after dividing all terms by 3.

 

Group terms for completing the square.

 

 
Divide the middle term, of both the x and y groups, by half and square it to complete the square. The value will fill in the blank space and you must add the amount to the constant D on the other side of the equals sign also.
general equation of a circle step 6
   
   

Completing the square for the y terms.

 

 

Solution in Standard Equation of the Circle form

with center (h,k) at (-1, 7/6)

solution

 

 

 


by Andrea Boggs

 

 



 

 





 

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