The centres of the circles x 2 + y 2 = 1 , x 2 + y 2 + 6 x − 2 y = 1 and x 2 + y 2 − 12 x + 4 y = 1 are Options: A . &nbsp same B . &nbsp Collinear C . &nbsp Non–collinear D . &nbsp None of these

Answer: Option B : B Centre are (0, 0), (-3, 1) and (6, -2) and a line passing through any two points say (0, 0) and (-3, 1) is y = − 1 3 x and point (6, -2) lies on it. Hence points are collinear.

The centres of the circles x2+y2=1, x2+y2+6x−2y=1 and x2+y2ȡ

Question

The centres of the circles $x^{2} + y^{2} = 1,$ $x^{2} + y^{2} + 6 x - 2 y = 1$ and $x^{2} + y^{2} - 12 x + 4 y = 1$ are

Options:

A . same

B . Collinear

C . Non–collinear

D . None of these

Answer: Option B
:
B
Centre are (0, 0), (-3, 1) and (6, -2) and a line passing through any two points say (0, 0) and (-3, 1) is

y = - \frac{1}{3} x

and point (6, -2) lies on it. Hence points are collinear.

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