Ask a New Question

Question

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

Answers

Reiny
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?
14 years ago

Related Questions

Find the equation of a hyperbola with foci of (0,8), and (0,-8) and Asymptotes of y=4x and... Find the points on the hyperboloid x2 −y2 +2z2 = 1 where the normal line is parallel to the line tha... Find the equation of a hyperbola which is generated by a point that moves so that the difference of... is 2x^2-5y^2+4x-6=0 a hyperbola or an ellipse? Find the equation of a hyperbola of the form x squared / M - y squared / N = 1 the transverse axis... Why might a writer use hyperbole? (1 point) They want to make a piece of writing more formal and ser... is this and example of Hyperbole Kade and Lula took slow, careful steps. All around them, the moo... Why might a writer use hyperbole?(1 point) Responses They want to emphasize a specific feeling o... It is personification, hyperbole, onomatopoeia, idiom, alliteration on the sense I haven’t seen you... Why might a writer use hyperbole?(1 point) Responses They want to make a piece of writing more forma...
Ask a New Question
Archives Contact Us Privacy Policy Terms of Use