Por favor, ayuda urgente con estos problemas sobre ecuacion de la circunferencia!?

A (0 ; - 6) B (1 ; 1) C (7 ; - 7) The equidistant point from A, B and C is the center of the circle that passes through the 3 points A, B and C. So you have to calculate the equation of the circle. The typical equation of a circle is: (x - xo)² + (y - yo)² = R²?

Where: xo: abscissa of center yo: ordinate of center R: radius of circle If the circle that passes through the 3 points A, B and C, it means that the coordinates of each point can verify the equation of the circle. With the point A (0 ; - 6) (x - xo)² + (y - yo)² = R²? Where: x = 0 and where y = - 6 (0 - xo)² + (- 6 - yo)² = R² xo² + 36 + 12yo + yo² = R² 36 + 12yo = R² - xo² - yo²?

Equation (1) With the point B (1 ; 1) (x - xo)² + (y - yo)² = R²? Where: x = 1 and where y = 1 (1 - xo)² + (1 - yo)² = R² 1 - 2xo + xo² + 1 - 2yo + yo² = R² 2 - 2xo - 2yo = R² - xo² - yo²? Recall (1): R² - xo² - yo² = 36 + 12yo 2 - 2xo - 2yo = 36 + 12yo xo = - 17 - 7yo?

Equation (2) With the point C (7 ; - 7) (x - xo)² + (y - yo)² = R²? Where: x = 7 and where y = - 7 (7 - xo)² + (- 7 - yo)² = R² 49 - 14xo + xo² + 49 + 14yo + yo² = R² 98 - 14xo + 14yo = R² - xo² - yo²? Recall (1): R² - xo² - yo² = 36 + 12yo 98 - 14xo + 14yo = 36 + 12yo 62 - 14xo + 2yo = 0 31 - 7xo + yo = 0?

Recall (2): xo = - 17 - 7yo 31 - 7.(- 17 - 7yo) + yo = 0 31 + 119 + 49yo + yo = 0 150 + 50yo = 0 3 + yo = 0? Yo = - 3 Recall (2): xo = - 17 - 7yo? Where: yo = - 3 xo = - 17 + 21?

Xo = 4 The coordinates of the required point are: M (4 ; - 3) Distance AM xAM = xM - xA = 4 - 0 = 4 yAM = yM - yA = - 3 + 6 = 3 AM² = xAM² + yAM² = (4)² + (3)² = 16 + 9 = 25? AM = 5 Distance BM xBM = xM - xB = 4 - 1 = 3 yBM = yM - yB = - 3 - 1 = - 4 BM² = xBM² + yBM² = (3)² + (- 4)² = 9 + 16 = 25? BM = 5 Distance CM xCM = xM - xC = 4 - 7 = - 3 yCM = yM - yC = - 3 + 7 = 4 CM² = xCM² + yCM² = (- 3)² + (4)² = 9 + 16 = 25?

CM = 5 You can see that: AM = BM = CM The equation of your circle is: (x - 4)² + (y + 3)² = 25? Where: xo: abscissa of center? 4 in your case yo: ordinate of center?

- 3 in your case R: radius of circle? 5 in your case.

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