For a hyperbola whose centre is at (1,2) and asymptotes are parallel to lines $2x+3y=0, x+2y=1$, then equation of hyperbola passing through (2,4) is

Let the asymptotes be $2x+3y+{\lambda }_1=0$ and  $x+2y+{\lambda }_2=0$
It will pass through centre (1,2). Hence,
${\lambda }_1=-8,{\lambda }_2=-5$
The equation of the hyperbola is.
(2x+3y-8)(x+2y-5)+$\lambda$ =0
It passes through (2,4),
(4+12-8)(2+8+5)+$\lambda$ =0
It passes through (2,4)
(4+12-8)(2+8-5)+ $\lambda$=-40
Hence, equation of hyperbola is
(2x+3y-8)(x+2y-5)=40