If a point P ( , ) on the line y =1 is such that the two distinct chords drawn on x^2+y^2- x-y=0 from P are bisected by the x -axis, then

Step-by-step solution

Given p =( , ) and Let C is the mid point of chord PQ, Let C =( , 0) =(- +2 ~h ,- ) Since lies on the circle. aligned & x ^2+ y ^2= x + y & (- +2 ~h )^2+(- )^2=(- +2 ~h )+( ) aligned aligned & or (- +2 ~h )^2+(-1)^2= (- +2 ~h )-1( =1) & 2 ~h ^2-3 h + ^2+1=0 aligned Since there are two distinct chords bisected by x -axis then for h to be real aligned & (-3 )^2-4.2 ( ^2+1 )>0 & ^2>8 aligned