Three distinct points are given in the 2-D plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point (–1, 0) Ps equal to $\frac{1}{3}$ . Then the locus of point A is,

Class: Grade 10

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x^{2} - y^{2} - \frac{5}{2} x + 1 = 0

x^{2} + y^{2} - \frac{5}{2} x + 1 = 0

x^{2} + y^{2} + \frac{5}{2} x + 1 = 0

None of these

answer is B.

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Detailed Solution

Let us consider the 3 points in 2 D be P, Q and R.
Let L = (1, 0) & M = (–1, 0).
ratio of the distance of any one of them from the point (1, 0) to the distance from the point (–1, 0) =
Let a point A (h, k) moves in such a way that.
…(i)
P, Q, R will lie on a locus of point A
Let (h, k) = (x1, y1) L = (1, 0) = (x2, y2)
& M = (–1, 0) = (x3 – y3)
put in eq (i)
S.O.B.S
Divide by 8.

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