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Question 1004009: Find two points on the circle x2 + y2 = 8 such that the slope of the
radius from (0, 0) to each point is 1.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find two points on the circle x2 + y2 = 8 such that the slope of the
radius from (0, 0) to each point is 1.
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It's obvious that the 2 points are on the diameter at an angle of 45 degs with the x-axis.
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Doing it the long way:
The tangent lines are perpendicular to the diameter.
The slope of the tangent lines at the 2 point is the negative inverse = -1
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The slope of the tangent line at any point on the circle is -x/y
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-x/y = -1
x = y
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x^2 + y^2 = 8
x^2 + x^2 = 8
x^2 = 4
x = ± 2
--> (2,2) and (-2,-2)
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