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Question 1042122: Find an equation of the set of all points equidistant from the origin and the line x + y – 1 = 0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find an equation of the set of all points equidistant from the origin and the line x + y – 1 = 0
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Let that point be (x,y)
It's distance from (0,0) is sqrt(x^2 + y^2)
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Every point on x + y -1 = 0 is (x,1-x)
Distance from (x,y) is sqrt((x-x)^2+(y-(1-x))^2) = y-(1-x)
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Equate those distances and solve for "y"::
y +x -1 = sqrt(x^2+y^2)
x^2 + y^2 = ((x+y)-1)^2
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x^2 + y^2 = (x+y)^2 - 2(x+y) + 1
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x^2 + y^2 = x^2 + 2xy + y^2 - 2x -2y + 1
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2xy - 2y = 2x -1
y(2x-2) = 2x-1
y = (2x-1)/(2x-2)
y = (1/2)[(2x-1)/(x-1)]
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Cheers,
Stan H.
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