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

Options

A. `3a`
B. `2a`
C. `a`
D. `4a`

Answer

C

Explanation

Given equation of the curve
`x^(2)y^(2)=a^(4)`
On differentiating the given equation, we get
`x^(2)2y(dy)/(dx)+y^(2)2x=0`
`implies(dy)/(dx)=-y/x`
`implies ((dy)/(dx))_((-a,a)) =-(a/(-a))=1`
`:.` Length of subtangent at the poing
`(-a,a)=y/(((dy)/(dx)))=a/1=a`