Given equation, 4x2+12xy+9y2+2gx+2fy−1=0 Since, general second-degree equation ax2+2hxy+by2+2gx+2fy+c=0 represents a pair of straight lines, if ∆=abc+2fgh−bg2−ch2−af2=0 Here, a=4,b=9,h=6 So, ∆=4×9×c+2fg×6−9g2 ‌−c(6)2−4f2=0 ‌=36c+12fg−9g2−36c−4f2=0 ‌=12fg−9g2−4f2=0 ⇒‌‌−(3g−2f)2=0⇒3g−2f=0 ⇒‌