The length of the subtangent to the curve `x^(2)+xy+y^(2)=7` at `(1,-3)`

Options

A. 3
B. 5
C. 15
D. `3/5`

Answer

C

Explanation

Given `x^(2)+xy+y^(2)=7`
`implies2x+x (dy)/(dx)+y+2y(dy)/(dx)=0`
`implies(dy)/(dx)=-((2x+y))/((x+2y))`
Length of subtangent `=|y (dx)/(xy)|=(-y(x+2y))/(2x+y)`
Length of subtangent at `(1,-3)` is
`|(-(-3)(1-6))/(2-3)|=|(3(-5))/(-1)|=15`