If the tangent at P on the curve `x^(m)y^(n)=a^(m+n)` meets the coordinate axes at A and B, then is :

Options

A. `("abscissae")^(2)`
B. `("ordinate")^(2)`
C. abscissa
D. ordinate

Answer

C

Explanation

We have,
`x^(m)y^(n) =a^(m+n)`
`rArr m log_(e)x + nlog_(e)y=(m+n) log_(e)a`
`rArr (m)/(2) + (n)/(y)(dy)/(dx)=0 " " ` [Differentiating w.r.t. x]
`rArr (dy)/(dx) = -(my)/(nx)`
`therefore " Length of the subtangent"=|(y)/((dy)/(dx))|=|y xx (nx)/(my)|=(n)/(m) |x| prop x`