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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) CircleI have been asked this question in an international level competition.My question is based upon Loci of Points topic in section Lettering Practice, Scales & Curves of Civil Engineering Drawing

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)^2or, 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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