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

1.	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
Answer» 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

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

Answer»

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