If the tangent to the curve `x y+a x+b y=0` at `(1,1)` is inclined at an angle `tan^(-1)2` with x-axis, then find `aa n db ?`

Options

A. `a=1, b=2`
B. `a=1,b=-2`
C. `a=-1,b=2`
D. `a=-1,b=-2`

Answer

B

Explanation

The point (1, 1) lies on the curve `xy +ax+by=0`
`therefore a+b= -1" …(i)" `
Now, `xy+ax+by=0`
`rArr x(dy)/(dx) +y+a+b(dy)/(dx)=0`
`rArr ((dy)/(dx))_((1","1)) = -(a+1)/(b+1) " ...(ii)" `
Since the tangent makes an angle `tan^(-1)2` with x-axis.
`therefore ` Slope of the tangent` = 2`
`rArr 2= -(a+1)/(b+1) rArr a+2b= -3 " ...(iii)" `
Solving (i) and (iii), we get `a=1, b= -2`