Equation 6x2−5xy+y2=0 represents____________________
Pair of distinct straight lines
Given equation is a homogeneous equation of second degree so, it represents a pair of straight line passing through origin.
Comparing the equation with ax2+2hxy+by2=0
We obtain a=6, b=1, h= −52
h2−ab=254−6=14
h2−ab>0⇒h2>ab
h2>ab
Hence, given equation represents a pair of distinct straight lines passing through the origin.
Option C is correct.