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Prove that for the curve y=be^(x//a) , ...

Prove that for the curve `y=be^(x//a)` , the subtangent is of constant length and the sub-normal varies as the square of the ordinate .

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The given curve is `y=be^(x//a)`
Differentiating it , we have
`(dy)/(dx)=(b)/(a)e^(x//a)=(y)/(a)`
Length of subtangent ` =(y)/(dy//dx)=(y)/(y//a)=a=`constant
Again length of subnormal `=y.(dy)/(dx)=y.(y)/(a)=(y^(2))/(a)`
i.e. subnormal ` prop y^(2)`
i.e. subnormal `prop` square of the ordinate .
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