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Find the equation of the pair of lines passing through the point (1, 1) and 1. parallel to the lines x2 − 5xy + 6y2 = 0. 2. perpendicular to the lines x2 − 5xy = 6y2 = 0. |
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Answer» The lines represented by x2 − 5xy + 6y2 = 0 are x − 2y = 0 and x − 3y = 0. we get the following: 1. Equation of the pair of lines passing through (1, 1) and parallel to the lines x − 2y = 0 and x − 3y = 0 is (x − 1)2 −5 (x − 1) (y − 1) + 6(y − 1)2 = 0 x2 − 5xy + 6y2 + 3x − 7y + 2 = 0 2. Equation of the pair of lines passing through (1, 1) and perpendicular to the lines 6(x − 1)2 + 5 (x − 1) (y − 1) + (y − 1)2 = 0 6x2 + 5xy + y2 − 17x − 7y + 12 = 0 |
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