If two lines x+(a-1) y=1 and 2 x+ a ^2 y=1( a R - 0,1 ) are perpendicular, then the distance of their point of intersection from the origin is

Step-by-step solution

Given equations of lines aligned & x+(a-1) y=1 & 2 x+a^2 y=1 aligned Slope of x+(a-1) y=1 is -1 a-1 and slope of 2 x+a^2 y=1 is -2 a^2 Given lines are perpendicular aligned & Product of slope =-1 & -1 (a-1) -2 a^2 =-1 & 2 a ^2( a -1) =-1 & a ^3- a ^2=-2 & a ^3- a ^2+2=0 & ( a +1) ( a ^2-2 a +2 )=0 & a =-1, a ^2-2 a +2=0 & a^2-2 a+2 0 [ a R - 0,1 ] & a=-1 aligned Equations will be aligned & x-2 y=1 & 2 x+y=1 aligned Point of intersection is ( 3 5 , -1 5 ) Distance of point of intersection from origin aligned & = (0-