December 15th, 2013, 04:00 AM  #1 
Member Joined: Nov 2012 Posts: 61 Thanks: 0  parabola
Tangents are drawn from (4,0) to . Radius of circles that would touch these tangents and corresponding chord of contact, can be equal to 
December 15th, 2013, 10:42 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,373 Thanks: 2010 
If tangent is y = m(x + 4), m²(x + 4)² = 16x has a repeated root (zero discriminant), so (8m²  16)²  64m^4 = 0, which implies m = ±1. The points of contact are (4, ±, so the chord of contact has equation x = 4. Can you now show that the circle's radius can be 8(?2 + 1)? Quick followup question: what integer value, if any, can the radius have? 

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