2

1

Let the equation of chord be y=mx+c

So combine equation of **pair of straight line** that passes through the origin and point of intersection of chord and curve is:

put value of 1 from the chord:

1=(y-mx)/c

3x^{2}-y^{2}-(2x+4y)(y-mx)/c=0

(3c+2m)x^{2 }+ (4m-2)xy +(-c-4)y^{2} =0

**these lines are perpendicular, so a+b =0**

3c +2m -c-4 =0

2=m*1 +c

compare this with the chord y=mx +c

so it will always pass through the fixed point:

** (1,2)**