Question

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

Answer 1

Answer:

$x^{2} +y^{2} +(-8)\times x+ (-6)\times y = 0$  

Step-by-step explanation:

General equation of circle is $x^{2} +y^{2} +2\times g \times x+2\times f\times y+c = 0$   ---------------------(1)

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

Substitute (1,7) in (1),

1 + $7^{2} +2\times g\times 1 + 2\times f\times 7 +c$ =0

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

Substitute (8,6) in (1),

$8^{2} + 6^{2} +2\times g \times 8+2\times f\times 6 +c=0$

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

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

$7^{2} + (-1)^{2} +2\times g \times 7+2\times f\times (-1) +c=0$

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

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

g = -4

f = -3

c = 0

Equation of circle is

$x^{2} +y^{2} +(-8)\times x+ (-6)\times y = 0$