Question

A point P moves in such a way that the ratio of its distances from two coplanar points is always fixed number $( \neq 1 )$. Then its locus is

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

Answer 1

Answer: (B)

Circle

Answer 2

Let two coplanar points are (0, 0) and (a, 0) and coordinates of point P is (x, y).

Under given conditions,

we get $\frac { \sqrt { x ^ { 2 } + y ^ { 2 } } } { \sqrt { ( x - a ) ^ { 2 } + y ^ { 2 } } } = \lambda$

(where $\lambda$ is any number and $\lambda \neq 1$ )

⇒ $x ^ { 2 } + y ^ { 2 } = \lambda ^ { 2 } \left[ ( x - a ) ^ { 2 } + y ^ { 2 } \right]$

⇒ ,

which is equation of a circle