orthogonal trajectories - sci.math

Message from discussion orthogonal trajectories

The World Wide Wade

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More options Jul 24, 10:53 am

Newsgroups: sci.math

From: The World Wide Wade <aderamey.a...@comcast.net>

Date: Wed, 23 Jul 2008 19:53:20 -0700

Local: Thurs, Jul 24 2008 10:53 am

Subject: Re: orthogonal trajectories

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In article
<6fc9fdd6-dead-4bb1-9f3d-0c749553c...@8g2000hse.googlegroups.com>,

conrad <con...@lawyer.com> wrote:
> I'm showing that a given family of curves are
> orthogonal trajectories of each other.

> I have the two curves:
> x^2 + y^2 = ax
> x^2 + y^2 = by

> It is said that the two circles intersect
> at the origin. How is this evident
> other than by plugging in 0?

Complete the square in x^2 + y^2 = ax to see you have a circle of
radius __ centered at __. This will immediately tell you the circle
goes thru the origin, as well as what the tangent line at the origin
has to be. Same with the other circle.

Alternately, you could down a couple of pints of Guinness and then see
what occurs to you.

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