HALLAR LA ECUACIÓN DE LA CIRCUNFERENCIA QUE CONTIENE A LOS PUNTOS Y GRAFICAR : a) A(12, - 5), B(1, 2) C(1, - 8)?

Veamos la ecuación general de la circunferencia

<img src="https://tex.z-dn.net/?f=%20%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2%5C%5C%20%5C%5C%20x%5E2%2By%5E2-2%28xh%2Byk%29%2B%28h%5E2%2Bk%5E2%29%3Dr%5E2%5C%5C%20%5C%5C%20x%5E2%2By%5E2-2%28xh%2Byk%29%3Dr%5E2-%28h%5E2%2Bk%5E2%29%5C%5C%20%5C%5C%20A%3D%2812%2C-5%29%3A%20169-2%2812h-5k%29%3Dr%5E2-%28h%5E2%2Bk%5E2%29%5C%5C%20%5C%5C%20B%3D%281%2C2%29%3A%205-2%28h%2B2k%29%3Dr%5E2-%28h%5E2%2Bk%5E2%29%5C%5C%20%5C%5C%20C%3D%281%2C-8%29%3A%2065-2%28h-8k%29%3Dr%5E2-%28h%5E2%2Bk%5E2%29%5C%5C%20%5C%5C%20%5C%5C%20%5Ctext%7BSi%20restamos%20las%20dos%20%5C%27ultimas%20ecuaciones%20tenemos%3A%7D%5C%5C%20%5C%5C%20%2060-2%28-10k%29%3D0%5C%5C%20%5Cboxed%7Bk%3D-3%7D%5C%5C%20%5C%5C%20%5Ctext%7BLuego%20tenemos%20el%20siguiente%20sistema%20de%20ecuaciones%3A%7D%5C%5C%20%5C%5C%20%5Cbegin%7Bcases%7D%20139-24h%3Dr%5E2-%28h%5E2%2B9%29%5C%5C%2017-2h%3Dr%5E2-%28h%5E2%2B9%29%20%5Cend%7Bcases%7D%5C%5C%20%5C%5C%20%5Ctext%7BPor%20igualaci%5C%27on%20se%20deduce%20%7D%5Cboxed%7Bh%3D%5Cdfrac%7B61%7D%7B11%7D%7D%20" />

Luego <img src="https://tex.z-dn.net/?f=%20%5Cboxed%7Br%5E2%3D%5Cdfrac%7B5525%7D%7B121%7D%7D%20" />

Por ende la ecuación de la circunferencia es

<img src="https://tex.z-dn.net/?f=%20%5Cboxed%7B%5Cleft%28x-%5Cdfrac%7B61%7D%7B11%7D%5Cright%29%5E2%2B%28y%2B3%29%5E2%3D%5Cdfrac%7B5525%7D%7B121%7D%7D%20" />.