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Re: Identifying a curve
Posted:
Jan 10, 2008 5:49 PM


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



