Question 5 - A-Level Maths

5 A circle with centre $C$ has equation $$( x - 5 ) ^ { 2 } + ( y + 12 ) ^ { 2 } = 169$$

Write down:
1. the coordinates of $C$;
2. the radius of the circle.
1. Verify that the circle passes through the origin $O$.
2. Given that the circle also passes through the points $( 10,0 )$ and $( 0 , p )$, sketch the circle and find the value of $p$.
The point $A ( - 7 , - 7 )$ lies on the circle.
1. Find the gradient of $A C$.
2. Hence find an equation of the tangent to the circle at the point $A$, giving your answer in the form $a x + b y + c = 0$, where $a , b$ and $c$ are integers.