Find the centre of the circle passing through
Asked by admin @ in Math viewed by 297 People
find the centre of a circle passing through the points (3,-7),(3,3),(6,-6). want the answer for 4 marks
Answered by admin @
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)
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