a quick question (1 Viewer)

[Sirius Black]

A point P on the rectangular hyperbola xy=4 has a tangent cutting x-axis at Q. From Q draw a line perpendicular to the tangent at P and this line cuts the hyperbolar at R, S. M is the midpoint of RS.
hmm, the locus of M is found to be y=-4/x and what would be the restriction on this locus?

I found the restriction should be t>1 or t<-1 but the sample answer simply states that t=/=0

 

[Jumbo Cactuar]

A point P on the rectangular hyperbola xy=4 has a tangent cutting x-axis at Q. From Q draw a line perpendicular to the tangent at P and this line cuts the hyperbolar at R, S. M is the midpoint of RS.
hmm, the locus of M is found to be y=-4/x and what would be the restriction on this locus?

I found the restriction should be t>1 or t<-1 but the sample answer simply states that t=/=0

I found the locus to be; y = - (4x)^1/3, x=/=0

which makes sense if you consider xy=4 as y or x -> 0 or infinity since the MP -> 0.

I can post calc if you want.

 

[samuelblayden]

that is a quick question

 

[Jumbo Cactuar]

that is a quick question

So quick it required two days to reply!

 

[Jumbo Cactuar]

Oh, not working then ... I was trying to make a signature randomiser, but evidently it does work too well. Works best for IE, shittest for firefox.

 

[Jumbo Cactuar]

Actually its all on a pretty poor server which drops out periodically, but hey - you can't complain with free

 

[Jumbo Cactuar]

Materials Science AND Chemistry.