3 A circle \(C\) has equation
$$x ^ { 2 } + y ^ { 2 } - 10 x + 14 y + 25 = 0$$
- Write the equation of \(C\) in the form
$$( x - a ) ^ { 2 } + ( y - b ) ^ { 2 } = k$$
where \(a , b\) and \(k\) are integers.
- Hence, for the circle \(C\), write down:
- the coordinates of its centre;
- its radius.
- Sketch the circle \(C\).
- Write down the coordinates of the point on \(C\) that is furthest away from the \(x\)-axis.
- Given that \(k\) has the same value as in part (a), describe geometrically the transformation which maps the circle with equation \(( x + 1 ) ^ { 2 } + y ^ { 2 } = k\) onto the circle \(C\).