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Question
Find the separate equation of the following pair of straight lines
6(x – 1)2 + 5(x – 1)(y – 2) – 4(y – 3)2 = 0
Solution
6(x – 1)2 + 5( x – 1)(y – 2) – 4(y – 3)2 = 0
Let x = x – 1 and y = y – 2
∴ The given equation becomes
6x2 + 5xy – 4y2 = 0
6x2 + 8xy – 3xy – 4y2 = 0
2x(3x + 4y) – Y(3x + 4y) = 0
(2x – y)(3x + 4y) = 0
2x – y = 0 and 3x + 4y = 0
Substituting for x and y, we have
2x – y = 0
⇒ 2(x – 1) – (y – 2) = 0
⇒ 2x – 2 – y + 2 = 0
⇒ 2x – y = 0
3X + 4Y = 0
⇒ 3(x – 1) + 4( y – 2 ) = 0
⇒ 3x – 3 + 4y – 8 = 0
⇒ 3x + 4y – 11 = 0
∴ The separate equations are
2x – y = 0 and 3x + 4y – 11 = 0
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