Question 10 - A-Level Maths

$$x ^ { 2 } + y ^ { 2 } + 4 x + p y + 123 = 0$$ where $p$ is a constant. Given that the point $( 1,16 )$ lies on $C$,

find
1. the value of $p$,
2. the coordinates of the centre of $C$,
3. the radius of $C$.
Find an equation of the tangent to $C$ at the point ( 1,16 ), giving your answer in the form $a x + b y + c = 0$, where $a , b$ and $c$ are integers to be found. \includegraphics[max width=\textwidth, alt={}, center]{de511cb3-35c7-4225-b459-a136b6304b78-31_33_19_2668_1896}