Posted by **help** on Saturday, November 27, 2010 at 4:30pm.

find all points on the hyperbola y=1/x, that are closest to the origin on (1/2,2)

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**Reiny**, Saturday, November 27, 2010 at 4:37pm
Let P(x,y) be the closest point

then if D is the distance, then

D^2 = x^2 + y^2

= x^2 + 1/x^2

2D dD/dx = 2x - 2/x^3

= 0 for a min of D

2x = 2/x^3

x^4 = 1

x = ± 1

if x=1, then y = 1

if x = -1, then y = -1

The two points closest to the origin are (1,1) and (-1,-1)

Where does the (1/2,2) come in?

Was that your answer?

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