Question

Write the general equation for the circle that passes through the points: (1, 7) (8, 6) (7, -1)

Answer 1

`x^(2) +y^(2) +(-8)* x+ (-6)* y = 0`

Explanation:

General equation of circle is
`x^(2) +y^(2) +2* g * x+2* f* y+c = 0` ---------------------(1)

This circle passes through the given three points, (1,7) , (8,6) and (7,-1).

Substitute (1,7) in (1),

1 +
`7^(2) +2* g* 1 + 2* f* 7 +c` =0

2g + 14f + c = -50 -------------(2)

Substitute (8,6) in (1),

`8^(2) + 6^(2) +2* g * 8+2* f* 6 +c=0`

16g + 12f + c = -100 -----------(3)

Substitute (7,-1) in (1),

`7^(2) + (-1)^(2) +2* g * 7+2* f* (-1) +c=0`

14g - 2f + c = -50 ---------------(4)

Solving (2),(3) amd (4) simultaneously,

g = -4

f = -3

c = 0

Equation of circle is

`x^(2) +y^(2) +(-8)* x+ (-6)* y = 0`