A line segment A B of length λ moves such that the points A and B remain on the periphery of a circle of radius λ . Then the locus of the point, that divides the line segment A B in the ratio 2 : 3 , is a circle of radius

Step-by-step solution

Given, A line segment A B of length λ moves such that the points A and B remain on the periphery of a circle of radius λ , Now taking the points on the circle of radius λ as B λ cos θ 1 , λ sin θ 1   &   A λ cos θ 2 λ sin θ 2 and taking the point P h , k which divides the line segment in A B of length λ in 2 : 3 Now plotting the diagram we get, Now, let O be the origin and radius of circle is λ and A B = λ and using distance formula