Consider the two circles $${(x - 1)^2} + {(y - 3)^2} = {r^2}$$ and $${x^2} + {y^2} - 8x + 2y + 8 = 0$$

What is the distance between the centres of the two circles?

Consider the two circles $${(x - 1)^2} + {(y - 3)^2} = {r^2}$$ and $${x^2} + {y^2} - 8x + 2y + 8 = 0$$

If the circles intersect at two distinct points, then which one of the following is correct?

Consider a circle passing through the origin and the points (a, b) and ($$-$$b, $$-$$a).

On which line does the centre of the circle lie?

Consider a circle passing through the origin and the points (a, b) and ($$-$$b, $$-$$a).

What is the sum of the squares of the intercepts cut-off by the circle on the axes?