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Problems in Plane Analytic Geometry: Difficult Problems with Solutions

Problem 1
If D||D', D:2x - y = 1 and D':(a - 1)x + 2y = x - 2, then find the value of a.
Problem 2
If D ⊥ D', D: (2a - 3)x + ay - 2 = 2y + 3a and D': (3a - 1)y + 2(3a + 1)x = a - 1 find the value of a.
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