Correct Answer - a
The equation of the tangent at P(x,y) is
` Y - y = (dy)/(dx) (X-x)`
`((y-x((dy)/(dx)))/(1-(dy)/(dx)),(y-x(dy)/(dx))/(1-(dy)/(dx)))rArr (y-x(dy)/(dx))/(1-(dy)/(dx))=1`
`rArr" "y-x (dy)/(dx)=1-(dy)/(dx)`
`rArr" "(dx)/(x-1)=(dy)/(y-1)`
On integrating, we get
`(x-1)=C(y-1) rArr C=((x-1)/((y-1))`