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प्रश्न
A point P moves so that P and the points (2, 2) and (1, 5) are always collinear. Find the locus of P.
उत्तर
Let P (x1, y1) be any point on the locus and A (2,2) B (1,5) are the fixed points.
Given that the points P, A, B are collinear.
⇒ Area of Δ PAB = 0
⇒ `1/2 [x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2)] = 0`
⇒ `1/2 [x_1 (2 - 5) + 2 (5 - y_1) + 1 (y_1 - 2)] = 0`
⇒ `1/2 [x_1 (-3) + 2 (5 - y_1) + 1 (y_1 - 2)] = 0`
⇒ `1/2 [- 3x_1 + 10 - 2y_1 + y_1 - 2] = 0`
⇒ `1/2 [- 3x_1 - y_1 + 8] = 0`
⇒ - 3x1 - y1 + 8 = 0
⇒ 3x1 + y1 - 8 = 0
∴ Locus of (x1, y1) is 3x + y - 8 = 0
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