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January 6th, 2012, 08:43 AM  #1 
Senior Member Joined: Jan 2012 Posts: 159 Thanks: 0  Find The Intersections Of A Circle and A Line
Find the longest and shortest distances from the point (7,12) to the circle x^2 + y^2 + 2x + 6y  15 = 0. The circle is (x+1)^2 + (y+3)^3=25 I found the equation of the line through the circle center (1,3) and the point (7,12) to be y=(15/X1 To solve I just plugged the line into the circle and then used the quadratic formula to get the x coordinates of the intersections but I was curious if there was an easier way. The answers, btw, are 22 and 12. 
January 6th, 2012, 09:28 AM  #2 
Senior Member Joined: Jul 2011 Posts: 405 Thanks: 16  Re: Find The Intersections Of A Circle and A Line From figure Minimum (AB) = ACBC=AC5 Maximum (AD) = AC+CD=AC+5 Where AC is Distance between A(7,12) and C(1,3) 
January 6th, 2012, 10:21 AM  #3 
Senior Member Joined: Jan 2012 Posts: 159 Thanks: 0  Re: Find The Intersections Of A Circle and A Line
Thanks panky! Much easier than the way I did it and so obvious (once it is explained of course )


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