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Re: Identifying a curve
Posted:
Jan 10, 2008 5:49 PM
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Steven <dixonlisauk@yahoo.co.uk> wrote:
> Suppose you drew a circle of radius 200 mm on a piece of paper with a
> compass and keeping the same centre point you moved the pencil point in
> at five mm increments so as to create ten circles each five mm less
> radius to the one outside of it. Now you also draw ten straight lines (
> running up the page as it were ) each five mm apart and position these
> lines so as they cut through the circles with the extreme left line being
> tangential with the inner circle and the extreme right line being 50 mm
> to the right and of course 50mm nearer the centre point of the circle.
> What you end up with is a series of intersections that when you connect
> with a line forms a curve. If you knew the initial properties of the
> circle and the straight lines could you determine the radius of this new
> curve?
Radius? If I have interpreted your question correctly, then the new curve
is a parabola with its axis horizontal and passing through the centre of
the circles and with its vertex 2.5mm left of that centre. Specifically,
with a coordinate system imposed, having its origin at the centre of the
circles, an equation of the parabola is y^2 + 10x + 25 = 0.
David
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