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1. General equation of a pair of straight lines passing through the origin
ax^{2} + 2hxy + by^{2} = 0
2. General equation of a pair of straight lines
ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c = 0.
3. Angle between a pair of straight lines passing through the origin
Acute angle between lines
tan q =

2
a + b
4. Condition for the equation ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c = 0 to represent a pair of lines
a
h
g
b
f
c
= 0