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do pair of staight lines always intersect?if no then how do we know whether parallel pair of straight lines are homogeneous or not

do pair of staight lines always intersect?if no then how do we know whether parallel pair of straight lines are homogeneous or not

Grade:12th pass

1 Answers

Vikas TU
14149 Points
7 years ago
Analgebric eqn. is homogenous eqn. if the sum of the powers of x and y in each term is equal to 2.
 
ax^2 + 2hxy + by^2 = 0
is the general form of a homogeneous eqn. of second degree in x and y and it represents strt. lines passing through the origin and these lines will be real and distinct if 
  1. h^2 > ab
  2. real aand coincide if h = ab
  3. if h^2 = ab then these lines will be coincide.
  4. if a+b =0 then two lines will be perpendicular to each other

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