Circle And System Of Circles Question 281
Question: A point P moves in such a way that the ratio of its distance from two coplanar points is always a fixed number $ (\ne 1) $ . Then its locus is
[IIT 1982]
Options:
A) Straight line
B) Circle
C) Parabola
D) A pair of straight lines
Show Answer
Answer:
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}+( \frac{{{\lambda }^{2}}}{{{\lambda }^{2}}-1} )(a^{2}-2ax)=0 $ , which is the equation of a circle.
BETA
