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

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?
Respond to this Question
Similar Questions

math
how do you find the coordinates of the point (x, y, z) on the plane z = 1 x + 1 y + 2 which is closest to the origin 
Math
Find an equation of the hyperbola with its center at the origin. vertices:(3,0)(3,0) Foci (5,0)(5,0) My answer was x^2/3  y^2/22 = 1. I do not know how to find a. 
Physics
The figure below shows two pint charges, each of 2Q, fixed on the yaxis at y = +a and at y = a . A third points charge Q is placed on the xaxis at x = 2a . Express all algebraic answers in terms of Q, a, and fundamental constants. … 
math30
The equation of the hyperbola is (x3)^2/4  (y+1)^2/16 =1. What is the range? 
algebra
find an equation that models the path of a satelite if its path is a hyperbola, a=55,000km and c=81,000km assume that the center of the hyperbola is the origin and the tranverse axis is horizontal 
agebra
Can someone please help me.. find an equation that models the path of a satelite if its path is a hyperbola, a=55,000km and c=81,000km assume that the center of the hyperbola is the origin and the tranverse axis is horizontal 
Calculus
a hyperbola passing through (8,6) consists of all points whose distance from the origin is a constant more than its distance from the point (5,2). find the slope of the tangent line to the hyperbola at (8,6). 
chuka university
given the eccentilisty and a point that lies on the hyperbola ,find the equation of the hyperbola center origin 
math
An ellipse and a hyperbola have the same foci, $A$ and $B$, and intersect at four points. The ellipse has major axis 50, and minor axis 40. The hyperbola has conjugate axis of length 20. Let $P$ be a point on both the hyperbola and … 
algebra
Please help with this problem: An ellipse and a hyperbola have the same foci, $A$ and $B$, and intersect at four points. The ellipse has major axis 50, and minor axis 40. The hyperbola has conjugate axis of length 20. Let $P$ be a …