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Question 1030424: 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 stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find all points (x,y) that are 13 units away from the point (2,7) and that lie on the line x - 2y = 10.
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13 units away is a circle ::
(x-2)^2 + (y-7)^2 = 13^2
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lie on the line::
x = 2y+10
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Substitute into the circle equation:
(2y+10-2)^2 + (y-7)^2 = 169
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(2y+8)^2 + (y-7)^2 = 169
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4y^2 + 32y + 64 + y^2 - 14y + 49 = 169
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5y^2 + 18y -56 = 0
(y-2)(5y+28) = 0
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y = 3 or y = -28/5
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x = 2*3+10 = 16 or x = 2(-28/5)+10 = (-56/5)+ 10 = -6/5
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Points:: (16,3) ; (-6/5,-28/5)
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Cheers,
Stan H.
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