Question

escreva a equação reduzida da circunferencia que passa pelos pontos A(3,0), B (-1,2) e C (4,-3)

Answer 1

(x-a)²+(y-b)²=r²

(3-a)²+(0-b)²=r² ==> 9-6a+a²+b²=r² (i)

(-1-a)²+(2-b)²=r² ==> 1+2a+a²+4-4b+b²=r² (ii)

(4-a)²+(-3-b)²=r² ==> 16-8a+a²+9+6b+b²=r² (iii)

(i)=(ii)

9-6a+a²+b² = 1+2a+a²+4-4b+b²

4-6a = 2a-4b

8a=4+4b

a=(1+b)/2

(ii)=(iii)

1+2a+a²+4-4b+b² = 16-8a+a²+9+6b+b²

-10b= 20-10a

-10b=20 -10 * (1+b)/2

-10b=20-5-5b

5b=-15 ==>b=-3

a=(1+b)/2=(1-3)/2 =-1

9-6a+a²+b²=r² ==> 9+6+1+9=r² ==> r²=25 ==>r=5

(x+1)²+(y+3)²=25 é a resposta