ax² + 2hxy + by² + 2gx + 2fy + c = 0 represents a pair of straight lines if :
abc + 2fgh − af² − bg² − ch² = 0, i.e. if 
= 0.
Such an equation is obtained again by multiplying the two equation of lines
(a 1 x + b 1 y + c 1 ) (a 2 x + b 2 y + c 2 ) = 0
(i) x 2 + 3xy + 2y 2 – 3x – 3y = 0 represents two lines whose equation are
Text Solution
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(i)a (ii)a
Sol- 12x 2 – 10xy + 2y 2 + 11x – 5y + k = 0
Δ = 0
abc + 2fgh – af 2 – bg 2 – ch 2 = 0
12.2.k + 2 
. 
(–5) – 12 
– 2 
– k (25) = 0 ⇒ k = 2
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