July 15th, 2010, 10:38 AM  #1 
Senior Member Joined: Apr 2009 Posts: 106 Thanks: 0  Analytical Geometry
Given P(2, 3) and circle (x3)^2 + (y3)^2 = 9, find the tangents (of the circle) through P.

July 15th, 2010, 11:42 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: Analytical Geometry
The distance from the point (2, 3) to the center of the circle is 5. The distance from the center of the circle to the point of tangency is 3. So, by Pythagoras, the distance from (2, 3) to the point of tangency (x, y) is 4, and that gives us the equation (x + 2)^2 + (y  3)^2 = 16. From this equation subtract the equation of the circle and solve for x. That will give you the xcoordinate of the point where the tangent meets the circle. Can you finish?

July 17th, 2010, 01:06 PM  #3 
Senior Member Joined: Apr 2009 Posts: 106 Thanks: 0  Re: Analytical Geometry
Yes. Thank you very much


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