Pair of Straight Lines - Formulas and Facts

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Last updated 3:18 AM on 10/9/26
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10 Terms

1
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General Formula of POSL

ax² + 2hxy + by² + 2gx + 2fy + c = 0

2
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Value of determinant of of line

abc + 2fgh - af² - bg² -ch²

3
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Angle Between Two lines (Homogenous)

tanθ = | 2√h² -ab| / a+b


4
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Condition for perpendicular (Homogenous)

a + b = 0

5
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Condition for coinciding (Homogenous)

h² - ab = 0

6
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Condition for real and distinct (Homogenous)

h² - ab > 0

7
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Condition for imaginary (Homogenous)

h² - ab < 0

8
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Angle Bisector (Homogenous)

x² - y²/a-b = xy/h

9
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Angle Bisector

[ (x-x₁)² - (y-y₁)² / a-b = (x-x₁)(y-y₁)/h

10
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Distance between two parallel lines

d = 2√(g²-ac/a(a+b) = 2√(f² - bc)/b(a+b)