SOLUTION: Find the points on the parabola y= x^2 closest to the point (0,1).

Question 1093826: Find the points on the parabola y= x^2 closest to the point (0,1).
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the points on the parabola y= x^2 closest to the point (0,1).
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the parabola is symmetrical about the y-axis and the point is on the y-axis.
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Label the point in Q1 on the parabola (h,k)
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d^2 = h^2 + (k-1)2
k = h^2
--> d^2 = k + k^2 - 2k + 1
d^2 = k^2 - k + 1
dk/dx = 2k - 1 = 0
k = 1/2
h = sqrt(2)/2
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--> (sqrt(2)/2, 1/2)
& (-sqrt(2)/2, 1/2)

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