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What curve does the locus represent if the locus of a moving point which is always equidistant from the points (2, -1) and (3, 2)?(a) Hyperbola(b) Straight line(c) Ellipse(d) Circle |
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Answer» The correct choice is (b) Straight line To elaborate: Let A (2, -1) and B (3, 2) be the given points and (x, y) be the co-ordinates of a point P on the required locus. Then, PA^2 = (x – 2)^2 + (y + 1)^2 and PB^2 = (x – 3)^2 + (y – 2)^2 By problem, PA = PB or, PA^2 = PB^2 or, (x – 2)^2 + (y + 1)^2 = (x – 3)^2 + (y – 2)^2 or, x^2 – 4x + 4 + y^2 + 2y + 1 = x^2 – 6x + 9 + y^2 – 4y + 4 or, 2x + 6y = 8 or, x + 3y = 4 ……… (1) Clearly, equation (1) is a first degree equation in x and y; hence, the locus of P is a straight line whose equation is x + 3y = 4. |
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