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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 = 312y 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: 20,474 Thanks: 2039 
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.

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.


Tags 
chord, circle, tangent 
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