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For the curve y^(n)=a^(n-1)x if the subn...

For the curve `y^(n)=a^(n-1)x` if the subnormal at any point is a constant, then `n` is equal to

A

1

B

2

C

`-2`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
B
Given `y^(n)=a^(n-1)x`
`impliesny^(n-1) . (dy)/(dx)=a^(n-1)`
`:. `Length of subnormal `=y(dy)/(dx)`
`=yxx(a^(n-1))/(ny^(n-1))=(a^(n-1))/(ny^(n-1))`
For constant subnormal `n` should be 2.
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