Question

The point on the y-axis which is equidistant from $A(-5,-2)$ and $B(3,2)$ is

• A. $(-4,0)$
• B. $(0,-2)$
• C. $(-2,0)$
• D. $(0,-4)$

Answer 1

The correct option is B $(0,-2)$

Let the point on the y-axis be $(0,y)$.
Distance between $(0,y)$ and $(-5,-2)=\sqrt{{(-5-0)}^2+{(-2-y)}^2}=\sqrt{25+4^2+y^2+4y}=\sqrt{y^2+4y+41}$
Distance between $(0,y)$ and $(3,2)=\sqrt{{(3-0)}^2+{(2-y)}^2}=\sqrt{9+4^2+y^2-4y}=\sqrt{y^2-4y+25}$
As the point $(0,y)$ is equidistant from the two points, both the distances calculated are equal.
$\sqrt{y^2+4y+41}=\sqrt{y^2-4y+25}$
$=>y^2+4y+41=y^2-4y+25$
$=>16=-8y$
$=>y=-2$

Thus, the point is $(0,-2)$.