All chord of the curve  $3x^2-y^2-2x+4y=0$  that subtends a right angle at the origin, passed through a fixed point whose coordinates are

Let the chord  $y=mx+c$ 

$3x^2-y^2-2\left(x-2y\right)\left(\frac{y-mx}{c}\right)=0$

i.e,  $x^2\left(3c+2m\right)-y^2\left(c-4\right)-2xy\left(1+2m\right)=0$

These are perpendicular

$\therefore 3c+2m-c+4=0$$\Rightarrow m+c=-2$

The mean the chord  $y=mx+c$  is always pass thorugh the point (1, -2)