Prove that the centres of the circles x^2+y^2-10x+9=0,x^2+y^2-6x+2y+1=0 and x^2+y^2-18x-4y+21=0 lies on a line; find the equation of line on which they lie?
1 Answer
Feb 10, 2018
Centre of the 1st circle can be found by rearranging it,
given,
or,
So,its centre lies at
for the 2nd one,
or,
So,its centre lies at,
Similiarly for the 3rd one,
or,
So,its centre lies at
So,the equation of a straight line passing through
or,
Now, putting
So,all three points lie on a starigh line,and the equation is stated above.