For the curve `xy=c^(2)` the subnormal at any point varies as

Options

A. `x^(3)`
B. `x^(2)`
C. `y^(3)`
D. `oo`

Answer

C

Explanation

Given `y=(c^(2))/x`
`implies(dy)/(dx)=c^(2)|-1/(x^(2))|`
`:.` Subnormal at any point `=|y.(dy)/(dx)|=|yxx(-(c^(2))/(x^(2)))|=|(-y^(3))/(c^(2))|`
`implies` Subnormal `prop y^(3)`.