A series of circles have their centres on a given straight line and their radii proportional tothe distances
of their corresponding centres from a given point in that line .find the envelope.plz solve this question step by step.
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Expert's answer
2012-12-03T11:00:56-0500
Let the given point is A. Let O is a center of typicalcircle. AC is the envelope. The radius of circle OC = AO * k. The angle ACO = 90 degrees. So, AC^2 + OC^2 = AO^2. AC = sqrt(AO^2 - CO^2) = sqrt(AO^2 - AO^2 * k^2) = AO *sqrt(1 - k^2).
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