Question 1 - A-Level Maths

A circle \(C\) has equation \(x ^ { 2 } + y ^ { 2 } - 10 x + 6 y - 15 = 0\).
1. Find the coordinates of the centre of \(C\).
2. Find the radius of \(C\).
  [0pt] [P3 June 2001 Question 1]
3. \(\mathrm { f } ( x ) \equiv a x ^ { 3 } + b x ^ { 2 } - 7 x + 14\), where \(a\) and \(b\) are constants.
Given that when \(\mathrm { f } ( x )\) is divided by \(( x - 1 )\) the remainder is 9 ,
write down an equation connecting \(a\) and \(b\). Given also that \(( x + 2 )\) is a factor of \(\mathrm { f } ( x )\),
find the values of \(a\) and \(b\).
[0pt] [P3 June 2001 Question 2]