The locus of the point at which two given unequal circles subtend equal angles is: (A) a straight line(B) a circle (C) a parabola (D) an ellipse

Options

A. a straihght line
B. a circle
C. a parabola
D. none of these

Answer

B

Explanation

Let two circles be `S =0` nd `S' =0` having radii `r_(1)` and `r_(2)`. Respectively
From the figure, we have
`(r_(1))/(sqrt(S_(1))) =(r_(2))/(sqrt(S'_(1)))`
`rArr S'_(1) r_(1)^(2) = r_(2)^(2) S_(1)`
`rArr S_(1) - ((r_(1))/(r_(2)))^(2) S'_(1) =0`
`:.` Locus of `P(h,k)`
`S -((r_(1))/(r_(2)))^(2) S' =0`, which represents the equation of a circle,