Question

Find center of circle passes through (6,-6),(3,-7),(3,3)

Answer 1

Let O (x, y) is the point of circle

if three given points A (3,-7) B (3,3) and C (6,-6)

we know distance between circumference and center is always same. i.e radius .

now,

OA^2=OB^2=OC^2

OA^2=OB^2

=>(x-3)^2+(y+7)^2=(x-3)^2+(y-3)^2

=>(x-3)^2-(x-3)^2=(y-3)^2-(y+7)^2

=> 0=(2y+4)(3)

=> y= -2

now again ,

OB^2=OC^2

(x-3)^2+(y-3)^2=(x-6)^2+(y+6)^2

put y=-2

=>(x-3)^2+(-2-3)^2=(x-6)^2+(-2+6)^2

=>(x-3)^2-(x-6)^2=16-25

=>(2x-9)(3)=-9

=> 2x= -3+9=6

=> x=3

hence center co-ordinate is (3,-2)

hope it helps you

comment if any doubts