Question 7 - A-Level Maths

Express the equation of the circle in the form $$( x - a ) ^ { 2 } + ( y - b ) ^ { 2 } = k$$
1. Write down the coordinates of $C$.
2. Show that the circle has radius $n \sqrt { 5 }$, where $n$ is an integer.
Find the equation of the tangent to the circle at the point $A$, giving your answer in the form $x + p y = q$, where $p$ and $q$ are integers.
The point $B$ lies on the tangent to the circle at $A$ and the length of $B C$ is 6. Find the length of $A B$.
[0pt] [3 marks]
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