A point `P` moves in such a way that the ratio of its distance from two coplanar points is always a fixed number `(!=1)` . Then, identify the locus of the point.

Options

A. Straight line
B. Circle
C. Parabola
D. A pair of straight lines

Answer

B

Explanation

Let two coplanar points are (0, 0) and (a, 0). Under given conditions, we get :
`sqrt(x^(2)+y^(2))/(sqrt((x-a)^(2)+y^(2)))=lambda, (lambda ne 1) ["where "lambda "is any number"]`
`rArr x^(2)+y^(2)+(lambda^(2))/(lambda^(2)-1))(a^(2)-2ax)=0`
Which is the equation of a circle.