The length of the subtangent to the curve `x^(2)y^(2)=a^(4)` at `(-a,a)` is

Options

A. `a/2`
B. `2a`
C. `a`
D. `a/3`

Answer

C

Explanation

Given `y^(2)=(a^(4))/(x^(2))implies2y(dy)/(dx)=(-2a^(4))/(x^(3))`
`implies(dy)/(dx)=(-a^(4))/(x^(3)y)`
At`(-a,a), (dy)/(dx)=(-a^(4))/(-a^(3).a)=1`
Now, length of subtangent to the given curve at `(-a,a)`
`=y/(dy//dx)=a/1=a`