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 Circles & Parabola (Posted on 2013-07-13)

Two circles with equal radii are externally tangent
at a point on the parabola y = x2. One of the circles
is also tangent to the x-axis while the other is also
tangent to the y-axis. Find the radius of both circles.

 See The Solution Submitted by Bractals No Rating

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 computer approximation | Comment 4 of 5 |
(In reply to a start by Charlie)

DEFDBL A-Z
CLS
FOR x0 = .8201941# TO .8201941# STEP .0000001#
y0 = x0 * x0
b = -1 / (2 * x0)

deltax = (x0 ^ 2 - x0) / (1 / (2 * x0) - 1)

newy = y0 + b * deltax
leftx = x0 - deltax
deltay = y0 - newy
dist = SQR(deltay ^ 2 + deltax ^ 2)
PRINT USING "###.#######"; x0; y0; leftx; newy; dist; newy - dist
PRINT x0 + deltax, y0 + deltay
NEXT

finds

0.8201941  0.6727184  0.4424272  0.4424272  0.4424272 -0.0000000
1.197960993479501           .903009516829121

The point on the parabola is (0.8201941, 0.6727184).
The radius of each circle is 0.4424272.
The left-hand circle is centered at (0.4424272, 0.9030095).
The right-hand circle is centered at (1.197961, 0.4424272).

 Posted by Charlie on 2013-07-13 17:07:42
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