The curve x y=c(c 0) and the circle x^2+y^2=1 touch at two points, then distance between the points of contacts is

Step-by-step solution

The curve x y=c and the circle x^2+y^2=1 touches each other so x^2+ c^2 x^2 -1=0 x^4-x^2+c^2=0 will have equal roots so (-1)^2-4 c ^2=0 4 c ^2=1 c^2= 1 4 c= 1 2 Roots of the equations x^4-x^2+ 1 4 =0 are x= 1 2 y = 1 2 . Clearly distance between the points of contact =2 units