Question

Find the centre of the circle passing through (5 -8) (2 -9) and (2 1)

Answer 1

Hope it helps..........

Answer 2

SOLUTION:-

Let the given points be;

⚫A(5,-8)

⚫B(2,-9)

⚫C(2,1)

Let the centre of the circle be O(x,y)

So,

OA= OB =OC [radii of circle]

Thus,

By applying the distance formula & equating the distance, we get;

OA = OB

=) (x-5)² + (y+8)² =(x-2)² +(y+9)²

=)x²+25-10x+y²+64+16y=x²+4-4x+y²+81+18y

=) 25+ 64 -4 -81= 10x -4x +18y-16y

=) 4= 6x + 2y

=) 3x + y= 2...........(1)

OB = OC

(x-2)² +(y+9)² =(x-2)² + (y-1)²

=) y² +81 +18y = y² +1 -2y

=) 80 = -18y - 2y

=) 80 = -20y

=) y= -4................(2)

Putting y= -4 in equation (1), we get;

=) 3x + y = 2

=) 3x +(-4) = 2

=) 3x -4 = 2

=) 3x= 2 +4

=) 3x= 6

=) x= 6/3

=) x= 2

Hence,

The coordinates of the centre are (2,-4).

Hope it helps ☺️