Question

A point in the space moves such that the ratio of its distances from two fixed points is a constant $(\ne 1)$, then the locus is

• A. Circle
• B. Sphere
• C. Plane
• D. Pair of circles

Answer 1

The correct option is B Sphere

A point moves such that the ratio of its distances from two fixed points is a constant but not equal to $1$.

$\therefore \frac{{(x-x_1)}^2+{(y-y_1)}^2}{{(x-x_2)}^2+{(y-y_2)}^2}=k$

$\Rightarrow (1-k)(x^2+y^2)-2(x_1-k{x}_2)x-2(y_1-k{y}_2)y+{x_1}^2+{y_1}^2-k{x_2}^2-k{y_2}^2=0$
Therefore, locus is circle.