You may be asked to show that two circles are touching, and say whether they're touching internally or externally. To do this, you need to work out the radius and the centre of each circle.

Show that the line \(y = 2x + 1\) intersects the circle \({x^2} + {y^2} - 6x - 7y + 9 = 0\) and determine the points of intersection. Therefore the line \(2x + 1 ...