SOLUTION: 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 po

Algebra ->  Graphs -> SOLUTION: 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 po      Log On


   

Question 1029905: 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.)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
From the distance formula, %28x-2%29%5E2+%2B+%28y-7%29%5E2+=+13%5E2
%282y+%2B+8%29%5E2+%2B+%28y-7%29%5E2+=+169, after substituting x = 2y + 10 into the equation above.
<==> 5y%5E2+%2B+18y+%2B113+=+169 after simplifying.
==> 5y%5E2+%2B+18y+-56+=0 ==> (5y+28)(y-2) = 0 ==> y = -28/5, 2
==> x = -6/5, 14.
Therefore the points are (-6/5, -28/5); (14,2).