Question

the centre of circle passing through the points (1,4) (4,1) and (-2,1) is ​

Answer 1

(1,1)

Is the correct answer

Answer 2

Given :

Three points : ( 1 , 4 ) , ( 4 , 1 ) and ( -2 , 1 ) .

To find :

The center of the circle passing through the given points .

Solution :

The equation of the circle is : $x^2$ + $y^2$ + 2gx + 2fy + c = 0

on putting the three points in the equation ,

2g + 8f + c = - 17              ......(i)

8g + 2f + c = - 17              .......(ii)

- 4g + 2f + c = - 5              ........(iii)

on solving the three equations ,

g = -1  

f =  -1

c = - 7

center of the circle = ( -g , -f )

=> center of the circle = ( 1 , 1 )

The center of the circle passing through the points (1,4) (4,1) and (-2,1) is (1,1) . ​