For the first question,If the circles are concentric,I got the ans.Here's my method.Let the center of the circles be origin(0,0) for convenience and their radii be a,b.

Then,eqn. of chord of contact from (bcosk,bsink) is S₀=0 that is xcosk+ysink=a²/b and it's eqn. when its midpoint is (x₀,y₀) is xx₀+yy₀=x₀²+y₀².Comparing the eqns.,we get,

x₀²+y₀²=(a²/b)² which is a circle with radius a²/b

Plz post the second question clearly.I couldn't understand it.