The points $A(-8,p)$ and $B(q,6)$ lie on the circle with equation

1. Given that $p>0$ and $p+q>0,$ find the values of $p$ and $q.$

2. Find the shortest distance from the centre of the circle to the chord $AB.$

Substitute the coordinates of $A$ into the equation of the circle and solve to find $p.$ Similar for $q.$

Once you have $p$ and $q$, you can draw a diagram to help with (b).

Here is the diagram, with a couple of clues: