My Math Forum Circle - tangent or chord?

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 April 20th, 2015, 06:24 AM #1 Newbie   Joined: Feb 2015 From: Scotland Posts: 20 Thanks: 0 Circle - tangent or chord? Hi All, I'm having a little difficulty with this problem. Any help would be appreciated. Show that the line 2y + x = 31 is a tangent to the circle x^2 + y^2 - 6x - 8y - 55 = 0 and determine point of contact. When I insert x = 31-2y into the circle equation I get 5y^2 - 124y + 720 = 0 and then b^2 - 4ac = 1336. With a tangent, you need it to equal 0. Can anyone see where I am going wrong? Thanks. Last edited by skipjack; April 20th, 2015 at 06:43 AM.
 April 20th, 2015, 06:49 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2203 You should have "120" instead of "124". Also, "1336" is incorrect (even if "124" is used). I suspect you swapped two digits in your intermediate working. Thanks from MathDino
 April 20th, 2015, 09:18 AM #3 Newbie   Joined: Feb 2015 From: Scotland Posts: 20 Thanks: 0 Great, simple calculation error. The 120 squared gives 14400 which is the same as 4ac. Thanks.

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