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 Post subject: HyperbolaPosted: Fri, 23 May 2003 10:26:27 UTC
Given hyperbola x^2-y^2=1

Find the point on the Oy-axis from which the tangent lines to the hyperbola are perpendicular

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 Post subject: Posted: Fri, 23 May 2003 11:57:58 UTC
 S.O.S. Oldtimer

Joined: Mon, 19 May 2003 07:15:29 UTC
Posts: 204
Location: Los Angeles

Here is a graph of your function:

Could you illustrate where the tangent lines might be, and where the location of the point you're interested in would be?
Just give a rough idea, then we'll figure out exactly where it should go.

_________________
My thoughts on Pi:
How I need a drink, alcoholic of course, drunk for happy feelings ...

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 Post subject: Posted: Fri, 23 May 2003 12:32:08 UTC
It is asked for the point on Oy-axis where the tangent lines to hyperbola are perpendicular...So the tangent lines depend on the point on the Oy-axis practically.Let me state an example:

1 line could be tangent in (-1,-1/2),the other in (1,1/2) and they're perpendicular in (0,1)

This is just an example to illustrate what i want,and is probably not true.

Also there is the possibility that such a point where the tangent lines are perpendicular,doesnt exist.But i have to bring a proof up for this...

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 Post subject: Posted: Fri, 23 May 2003 19:42:52 UTC
 S.O.S. Oldtimer

Joined: Tue, 20 May 2003 17:25:56 UTC
Posts: 235
Location: Israel
hi, try this:
let A(p;t) be one of the points on the Oy-axis from which the tangent lines to the hyperbola are perpendicular. try to express p by t or the opposite. if it'll go ok you will get some function and the "points on the Oy-axis from which the tangent lines to the hyperbola are perpendicular" will be located on it. then you can swich p and t to x and y if you want.
hope it helps.
Good Luck

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