My Math Forum Find The Intersections Of A Circle and A Line

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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/X-1 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) = AC-BC=AC-5 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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