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 December 15th, 2013, 04:00 AM #1 Member   Joined: Nov 2012 Posts: 61 Thanks: 0 parabola Tangents are drawn from (-4,0) to $y^2=16x$. Radius of circles that would touch these tangents and corresponding chord of contact, can be equal to $8(sqrt2+1) 8sqrt2-1 16 8sqrt2$
 December 15th, 2013, 10:42 AM #2 Global Moderator   Joined: Dec 2006 Posts: 18,686 Thanks: 1522 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 follow-up question: what integer value, if any, can the radius have?

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