Conic Challenge #14

Geometry Level 3

A stick of length 10 m slides on coordinate axes, then the locus of a point dividing this stick reckoning from x-axis in ratio 3:2 is a curve whose eccentricity is e.Find the value of 9 √ 5 ∗ e 9√5 * e .


The answer is 15.

Ninad Akolekar by Ninad Akolekar , 23, India

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2 solutions

Deepanshu Gupta
Feb 14, 2015

Use 2nd defination of ellipse "point which devides fixed length line in length ratio a:b then locus of point is ellipse with a as major and b as minor axis length " a=6 and b=4

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Anurag Singh
Jun 15, 2015

well consider at any instant while the stick falls its x intercept is X and y intercept is , since the lenght of the stick is constant thus we can conclude that; X^2 +Y^2=100 the co ordinates of mentioned point can be obtained by section formula I.e (2X/5,3Y/5) By using the point ^^ and the equation one can easily get the equation of ellipse and then the eccentricity

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