A) Straight line
B) Circle
C) Parabola
D) A pair of straight lines
Correct Answer: B
Solution :
Let two coplanar points are (0, 0) and (a, 0). Under given conditions, we get \[\frac{\sqrt{{{x}^{2}}+{{y}^{2}}}}{\sqrt{{{(x-a)}^{2}}+{{y}^{2}}}}=\lambda ,\ (\lambda \ne 1)\] (where \[\lambda \] is any number) \[\Rightarrow {{x}^{2}}+{{y}^{2}}+\left( \frac{{{\lambda }^{2}}}{{{\lambda }^{2}}-1} \right)\text{ }({{a}^{2}}-2ax)=0\], which is the equation of a circle.
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