JEE Main 2026 — 2 April, Morning Shift — Question 27

\begin{array}{*{35}{r}}{} & {{m}_{BC}}\times {{m}_{AH}}=-1 \\{} & ~\Rightarrow \text{ }\!\!~\!\!\text{ }{{m}_{BC}}=-\frac{1}{{{m}_{AH}}} \\{} & ~\Rightarrow {{m}_{BC}}=\frac{\beta -3}{\alpha -4}=0 \\\end{array}

$\Rightarrow \beta =3$ ${{m}_{AB}}\times {{m}_{CH}}=-1$

$\Rightarrow \frac{1}{4} \times \frac{\beta}{\alpha}=-1$

$\Rightarrow \beta=-4 \alpha$

$\Rightarrow \alpha=-\frac{3}{4}$

Vertex $C$ Is $\left(\frac{-3}{4}, 3\right)$

$\Rightarrow$ Vertex $C$ lies in second quadrant.

$\Rightarrow$ Option (4) is correct.