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August 16th, 2013, 04:32 PM   #1
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Circle

If there's a circle x + y = r (r > 0) and the line tangent to such circle has the equation y = a, determine the two real number answers for a.
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August 16th, 2013, 05:28 PM   #2
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Re: Circle

since y=a is horizontal, the coordinates of contact will be (0, r) and /(0, -r).
Thus a=r and a=-r
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August 16th, 2013, 07:52 PM   #3
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Eliminating y from the given equations, one gets x + a - r = 0.
This equation must have "equal roots" (zero discriminant), so a = r.
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August 16th, 2013, 09:49 PM   #4
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Re: Circle

You can also let x = 0 from which you get y = r = a immediately.

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August 16th, 2013, 11:16 PM   #5
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Without explaining why you take x = 0?
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August 16th, 2013, 11:34 PM   #6
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Re: Circle

Wonder why Slipper posted that problem...quite obvious that a circle radius r centered at origin
has 2 tangent points (to horizontal lines) at (0,r) and (0,-r).
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August 17th, 2013, 01:07 AM   #7
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Re:

Quote:
Originally Posted by skipjack
Without explaining why you take x = 0?
I had a hunch you would say that. I guess we can plug in the constant 'a' , take the derivative , set it to zero to confirm the horizontal tangents indeed occur when x = 0 , then go back and let x = 0 to get y = r = a.

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