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A ladder 12 units long slides in a vertical plane with its ends in contact with a vertical wall and a horizontal floor along the x-axis. If the locus of a point on the ladder 4 units from its foot is an ellipse, then the ratio of the length of the major axis to the minor axis is

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answer is 2.

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Detailed Solution

$G i v e n t h e l e n g t h o f l a d d e r = 12 = s T h e l o c u s o f a p o i n t o n t h e l a d d e r = 4 = k T h e e q u a t i o n o f t h e l o c u s o f a p o i n t f r o m o n e e n d i s \frac{x^{2}}{{(s - k)}^{2}} + \frac{y^{2}}{k^{2}} = 1 \Rightarrow \frac{x^{2}}{{(12 - 4)}^{2}} + \frac{y^{2}}{4^{2}} = 1 \Rightarrow \frac{x^{2}}{64} + \frac{y^{2}}{16} = 1 N o w a : b = 8 : 4 = 2$

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