Question

find the coordinates of the centre of the circle passing through the points A (-2,-3),B(-1,0) and C(7 -6). Also find the radius of this circle

Answer 1

Step-by-step explanation:

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

points A, B and C are on boundary of the circle.

there for, OA, OB, OC will be equal (all are radii of the circle)

OA²=(x+2)²+(y+3)²........(1)

OB²=(x+1)²+(y-0)².........(2)

OC²=(x-7)²+(y+6)².........(3)

by (1) and (2)

x²+4x+4+y²+6y+9=x²+2x+1+y²

4x-2x+6y+4+9-1=0

2x+6y+12=0

x+3y+6=0..... .. ..(4)

by (2) and (3)

x²+2x+1+y²=x²-14x+49+y²+12y+36

16x-12y-84=0

4x-3y-21=0............(5)

solve (4) and (5)

15y=45

y=3

put this value in (4), we get x=-15

to find radius of the circle put these values in (1), (2) or (3)

9

OB=√196+9=√205

Answer 2

here is the complete solution...hope it's helpful...do hit me brainliest and helpful