Given curve is
3x2−y2−2x+4y=0, let y=mx+c and the chords by homogenization, combined equation of lines passing through point intersection of chords and curve
3x2−y2−2x[y−mxc]+4y[y−mxc]=0
∵Itsubtends90∘attheorigin
⇒Coefficientofx2+coeff.ofy2=0
3+2mc+4c−1=0⇒mc+2c+1=0
⇒c=−(m+2)
Hence, y=mx+c can be converted to
y=mx−m−2
m(x−1)+(−y−2)=0
Which is of the form L1+λL2=0
⇒Pointofconcurrencywillbe(1,−2)
⇒|a|+|b|=3