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January 6th, 2012, 08:43 AM   #1
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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.
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January 6th, 2012, 09:28 AM   #2
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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)
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January 6th, 2012, 10:21 AM   #3
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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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