If the orthocentre of the triangle, whose vertices are$(1,2), (2,3),$ and $(3,1)$ is $\left(\mathrm{\alpha }, \mathrm{\beta }\right)$, then the quadratic equation whose roots are $\mathrm{\alpha }+4\mathrm{\beta } \mathrm{\&} 4\mathrm{\alpha }+\mathrm{\beta }$, is 

Equation of altitude  AD $\Rightarrow$x - 2y + 3 = 0
Equation of altitude BE $\Rightarrow$2x - y - 1 = 0
Orthocentre of the triangle  $=\left(\frac{5}{3},\frac{7}{3}\right)=(\mathrm{\alpha },\mathrm{\beta })$
Quadratic equation whose roots are $\mathrm{\alpha }+4\mathrm{\beta }=11 \mathrm{\&} 4\mathrm{\alpha }+\mathrm{\beta }=9,\text{ is }{\mathrm{x}}^2-20\mathrm{x}+99=0$