If the straight line 2 x+3 y-1=0, x+2 y-1=0 and a x+b y-1=0 form a triangle with origin as orthocentre, then (a, b) is equal to

Step-by-step solution

Here, point A is the intersection of line A B and A C so equation of line passing through A . This line passes through the orthocentre (0,0) , then aligned & -1- =0 & =-1 aligned On substituting =-1 in Eq. (i), we get x+y=0 as the equation of A D . Since A D B C , therefore -1 - a b =-1 Similarly, by applying the condition that B E is perpendicular to C A , we get Now, solving Eqs. (ii) and (iii), we get a=-8, b=8