If two distinct points lying at a unit distance from 4 x +3 y -10=0 and passing through x + y =4 are separated by a distance d , then the value of d is

Step-by-step solution

The point lie on x+y=4 Coordinates of point ( , 4- ) Distnace from 4 x+3 y-10=0 is 1 | 4 +3(4- )-10 4^2+3^2 |=1 | 4 +12-3 -10 5 |=1 aligned & | +2|=5 & +2= 5 & =3,-7 aligned at =3,4- =1 at =-7, 4- =11 The 2 points are (3,1) and (-7,11) d= (-7-3)^2+(11-1)^2 = 100+100=10 2