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A ladder of length L stands against a vertical wall. It is being slipped down against the wall. Find the locus of (a) a point which divides ladder 2:3 internally from floor side. (b) mid-point of ladder.
a) Say the point on the ladder is C(x,y). The ends of the ladder are A(a,0) B(0,b). Here, a and b are not constants as the ladder is slipping down.As C divides AB in 2:3,x = 3a/5y = 2b/5As length of ladder is constant,a^2 + b^2 = L^2(x/3)^2 + (y/2)^2 = (L/5)^2This is the locus. It is an ellipse.b) Mid point of ladder :D(x,y) is the midpoint.x = a/2y=b/2As a^2 + b^2 = L^2x^2 + y^2 = (L/2)^2It is a circle.ThanksBharat BajajIIT Delhiaskiitians faculty
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