Determine the equation of the circle that passes through three points, J ( − 3 , 2 ), K ( 4 , 1 ), and L ( 6 , 5 ).using systems like so: { ( x + 3 ) 2 + ( y − 2 ) 2 = r 2 ( x − 4 ) 2 + ( y − 1 ) 2 = r 2 ( x − 6 ) 2 + ( y − 5 ) 2 = r 2 After equating the expressions on the left hand side of each equation, expanding and simplifying, I found out that y = 7 x − 2. I decided to substitute the y into two of the expressions to solve for x. But it only gives me 50 x 2 − 50 x + 25 = 50 x 2 − 50 x + 25, which does not help.

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Determine the equation of the circle that passes through three points,   J  (  −  3  ,  2  ),   K  (  4  ,  1  ), and   L  (  6  ,  5  ).using systems like so:      {                            (          x          +          3                      )            2                    +          (          y          −          2                      )            2                    =                      r            2                                                (          x          −          4                      )            2                    +          (          y          −          1                      )            2                    =                      r            2                                                (          x          −          6                      )            2                    +          (          y          −          5                      )            2                    =                      r            2                                  After equating the expressions on the left hand side of each equation, expanding and simplifying, I found out that   y  =  7  x  −  2. I decided to substitute the   y into two of the expressions to solve for   x. But it only gives me   50      x    2    −  50  x  +  25  =  50      x    2    −  50  x  +  25, which does not help.

Blaze Frank · Accepted Answer

Your procedure (modified a little) will work. From the first two equations, you got a linear equation in x and y. In the same way, from the last two equations, you can get a linear equation in x and y. Solve. Now you have the coordinates of the centre, and the rest is easy.Remark: The procedure will be clearer if you start by saying let (a,b) be the centre, and r the radius. Then write down your equations, but with a,b instead of x,y. These equations say that the three given points are all at distance r from the centre.

telegrafyx · Accepted Answer

Use the equation       x    2    +      y    2    +  2  g  x  +  2  f  y  +  c  =  0. Substitute those values, you will get three equations involving   g  ,  f  ,  c. Substituting the values back to the equation will be your equation. The answer will be       x    2    +      y    2    −  2  x  −  10  y  +  1  =  0 or   (  x  −  1      )    2    +  (  y  −  5      )    2    =  25

Determine the equation of the circle that passes through three points, J ( −<!-- −

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