Mathematics - Straight Lines Question with Solution | TestHub

Here, point $A$ is the intersection of line $AB$ and $AC$ so equation of line passing through $A$. $(x+2y-1)+\lambda (2x+3y-1)=0$ .....(i) This line passes through the orthocentre $(0,0)$, then $-1-\lambda =0$ $\Rightarrow \lambda =-1$ On substituting $\lambda =-1$ in Eq. $(i)$, we get $x+y=$ 0 as the equation of $AD$. Since $AD\perp BC$, therefore$-1\times -\frac{a}{b}=-1$ $\Rightarrow a+b=0$ ...(ii) Similarly, by applying the condition that $BE$ is perpendicular to $CA$, we get $a+2b=8$ ....(iii) Now, solving Eqs. (ii) and (iii), we get $a=-8$, $b=8$