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Answer to Question #16831 in Calculus for soni sharma

Question #16831
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.
Expert's answer
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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