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Find the separate equation of the lines represented by the following equation :

10(x + 1)2 + (x + 1)( y – 2) – 3(y – 2)2 = 0

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10(x + 1)2 + (x + 1)( y – 2) – 3(y – 2)2 = 0 …(1) 

Put x + 1 = X and y – 2 = Y

∴ (1) becomes

10x2 + xy – 3y2 = 0

10x2 + 6xy – 5xy – 3y2 = 0

2x(5x + 3y) – y(5x + 3y) = 0

(2x – y)(5x + 3y) = 0

5x + 3y = 0 and 2x – y = 0

5x + 3y = 0

5(x + 1) + 3(y – 2) = 0

5x + 5 + 3y – 6 = 0

∴ 5x + 3y – 1 = 0

2x – y = 0

2(x + 1) – (y – 2) = 0

2x + 2 – y + 2 = 0

∴ 2x – y + 4 = 0

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