Pair of Straight Lines

Question 1

What is the equation of pair of straight lines ?

Answer 1

The equation of a pair of straight lines is given by ax²+2hxy+by²
if h²-ab>=0 and m1+m2= -2h/b and m1m2 = a/b

Question 2

What is the angle between the lines represented by ax²+2hxy+by² = 0?

Answer 2

Angles between pair of straight lines is given by:
tan ∅ = m1-m2/ 1+ m1m2 = ±√4h²-4ab/ a+b
if a+b=0, lines are perpendicular
if h²=ab, lines are coincident

Question 3

What is the equation of the condition for a pair of straight lines from a second degree equation?

Answer 3

General equation of second degreee represent a pair of straight lines if : abc+2fgh-af²-bg²-ch²=0

Question 4

What is the point of intersection of pair of straight lines if h²≠ab?

Answer 4

The point of intersection of pair of straight lines if h²≠ab:
x1 = hf-bg / ab-h²
y1=gh-af / ab-h²

Question 5

What is the equation of pair of lines through the origin perpendicular to the pair of lines ax²+2hxy+by² = 0

Answer 5

bx²-2hxy+ay²=0