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 . (x+2 y-1)+ (2 x+3 y-1)=0 .....(i) This line passes through the orthocentre (0,0) , then -1- =0 =-1 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 a+b=0 ...(ii) Similarly, by applying the condition that B E is perpendicular to C A , we get a+2 b=8 ....(iii) Now, solving Eqs. (ii) and (iii), we get a=-8 , b=8