Find all points (x,y) that are 13 units away from the point (2,7) and that lie on the line x - 2y = 10. Give your answer as a list of points separated by semicolons, with the points ordered such that their x-coordinates are in increasing order. So "(1,-3); (2,3); (5,-7)" - without the quotes - is a valid answer format.)

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  1. all points (x,y) that are 13 units away from the point (2,7) defines a circle:

    (x-2)^2 + (y-7)^2 = 169

    so, the line x-2y=10 may intersect the circle in 0,1, or 2 points.

    So, plug x=2y+10 into the equation of the circle and see where the two graphs intersect.

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    posted by Steve
  2. see whether you get what wolframalpha does:^2+%2B+%28y-7%29^2+%3D+169,+x-2y%3D10

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    posted by Steve

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