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

(x+4)2+(y−2)2=20
  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: