Question

The centres of the circles x² + y² = 1, x² + y² + 6x – 2y = 1 and x² + y² – 12x + 4y = 1 are ______.

Options

• same

• collinear

• non-collinear

• none of these

Answer 1

The centres of the circles x² + y² = 1, x² + y² + 6x – 2y = 1 and x² + y² – 12x + 4y = 1 are collinear.

Explanation:

Centres of the circles are (0, 0), (– 3, 1) and (6, – 2) respectively.

Line passing through any two points say (0, 0) and (– 3, 1) is y = `1/3 x`

Point (6, –2) lies on it.

Hence, the centres are collinear.