August 16th, 2013, 04:32 PM  #1 
Member Joined: Aug 2013 Posts: 59 Thanks: 0  Circle
If there's a circle x² + y² = r² (r > 0) and the line tangent to such circle has the equation y = a, determine the two real number answers for a.

August 16th, 2013, 05:28 PM  #2 
Member Joined: Aug 2013 Posts: 32 Thanks: 1  Re: Circle
since y=a is horizontal, the coordinates of contact will be (0, r) and /(0, r). Thus a=r and a=r 
August 16th, 2013, 07:52 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,757 Thanks: 2138 
Eliminating y from the given equations, one gets x² + a²  r² = 0. This equation must have "equal roots" (zero discriminant), so a = ±r. 
August 16th, 2013, 09:49 PM  #4 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Circle
You can also let x = 0 from which you get y = ±r = a immediately. 
August 16th, 2013, 11:16 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,757 Thanks: 2138 
Without explaining why you take x = 0?

August 16th, 2013, 11:34 PM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  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). 
August 17th, 2013, 01:07 AM  #7  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Quote:
 

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