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)

- math -
**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?

## Answer this Question

## Related Questions

- Calculus - a hyperbola passing through (8,6) consists of all points whose ...
- math30 - The equation of the hyperbola is (x-3)^2/4 - (y+1)^2/16 =-1. What is ...
- algebra - find an equation that models the path of a satelite if its path is a ...
- agebra - Can someone please help me.. find an equation that models the path of a...
- Math - Find an equation of the hyperbola with its center at the origin. vertices...
- math - how do you find the coordinates of the point (x, y, z) on the plane z = 1...
- Physics - The figure below shows two pint charges, each of -2Q, fixed on the y-...
- math - Which point on the circle x^2+y^2-12x-4y=50 is closest to the origin? ...
- Math - Which point on the circle x^2+y^2-12x-4y=50 is closest to the origin? ...
- math - Find the equation of a hyperbola which is generated by a point that moves...

More Related Questions