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April 20th, 2015, 06:24 AM   #1
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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.
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April 20th, 2015, 06:49 AM   #2
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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.
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April 20th, 2015, 09:18 AM   #3
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Great, simple calculation error. The 120 squared gives 14400 which is the same as 4ac. Thanks.
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