3. A circle has centre \(C ( 3 , - 8 )\) and radius 10.
- Express the equation of the circle in the form
$$( x - a ) ^ { 2 } + ( y - b ) ^ { 2 } = k$$
- Find the \(x\)-coordinates of the points where the circle crosses the \(x\)-axis.
- The line with equation \(y = 2 x + 1\) intersects the circle.
- Show that the \(x\)-coordinates of the points of intersection satisfy the equation
$$x ^ { 2 } + 6 x - 2 = 0$$
- Hence show that the \(x\)-coordinates of the points of intersection are of the form \(m \pm \sqrt { n }\), where \(m\) and \(n\) are integers.
[0pt]
[BLANK PAGE]