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 November 25th, 2009, 10:07 PM #1 Newbie   Joined: May 2009 Posts: 25 Thanks: 0 Find equation of the common tangent to the parabolas Find equation of the common tangent to the parabolas y^2 = 4ax and x^2 = 4by November 26th, 2009, 01:22 PM #2 Global Moderator   Joined: Dec 2006 Posts: 21,114 Thanks: 2329 The tangent to the parabola y� = 4ax at the point (at�, 2at) has equation ty = x + at�. The tangent to the parabola x� = 4by at the point (2bu, bu�) has equation ux = y + bu�. If the above tangents have the same equation, tu = 1 and bu� = -at, so u� = -a/b. Hence u = �?(-a/b) and t = �?(-b/a), where "�?" specifies the real cube root. December 1st, 2009, 09:19 PM   #3
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Re: I couldnt understand the last 2 lines

Quote:
 Originally Posted by skipjack If the above tangents have the same equation, tu = 1 and bu� = -at, so u� = -a/b. Hence u = �?(-a/b) and t = �?(-b/a), where "�?" specifies the real cube root.

Please could u explain me how did u get tu = 1 , bu^2 = -at from the eg. of tangents.... December 1st, 2009, 11:13 PM #4 Global Moderator   Joined: Dec 2006 Posts: 21,114 Thanks: 2329 I multiplied the second equation by t, then compared it to the first equation. One term is already the same, and the equations I gave follow if the other two terms are the same. Tags common, equation, find, parabolas, tangent ,

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