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Let Ax^{2}+2Hxy +By^{2} +2Gx+2Fy+C=0, be the pair of st. lines.

condition to represent the pair of st. line is: ABC+2FGH -AF^{2}-BG^{2}– AF^{2}=0.

Our equation is ay^{2}+bxy+cx+dy=0

On comparing

A=0, H =b/2, B=a,G=c/2,F=d/2 and C=0.

0+bcd/4 -0-ac^{2}/4 =0

c.(bd-ac)=0

either c=0 or bd-ac=0.