The joint equation of a family of lines is always of second degree in x and y.
The joint equation of the straight lines a1x +b1y +c1 = 0 and a2x +b2y+ c2 = 0 is
(a1x +b1y +c1) (a2x +b2y+ c2) = 0
The equation ax² +2hxy+by² = 0 is known as homogeneous equation of second degree.
In a homogeneous equation of second degree, the sum of indices (exponents) of x and y in each term is equal to 2.
The homogeneous equation of second degree ax² +2hxy+by² = 0 represents a joint equation of two straight lines passing through the origin if h²≥ab.
If y = m1x and y = m2x are the lines represented by a homogeneous equation of second degree ax² +2hxy+by² = 0, then
(i) m1 =m2 = -2h/b
(ii) m1m2 = a/b
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