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Question: The centres of the circles \(x ^ { 2 } + y ^ { 2 } = 1\), \(x ^ { 2 } + y ^ { 2 } + 6 x - 2 y = 1\) ...

The centres of the circles x2+y2=1x ^ { 2 } + y ^ { 2 } = 1, x2+y2+6x−2y=1x ^ { 2 } + y ^ { 2 } + 6 x - 2 y = 1 and x2+y2−12x+4y=1x ^ { 2 } + y ^ { 2 } - 12 x + 4 y = 1 are.

A

Same

B

Collinear

C

Non-collinear

D

None of these

Answer

Collinear

Explanation

Solution

Centres are (0, 0), (–3, 1) and (6, –2) and a line passing through any two points say (0, 0) and (–3, 1) is y=−13xy = - \frac { 1 } { 3 } x and point (6, –2) lies on it. Hence points are collinear.