Question

A point $P$ moves such that its distances from $(1,2)$ and $(-2,3)$ are equal. Then the locus of $P$ is

• A. Straight line
• B. Parabola
• C. Ellipse
• D. Hyperbola

Answer 1

Answer: (A)

Straight line

Distance between two points is $\sqrt{{{(x}_2-x_1)}^2+{{(y}_2-y_1)}^2}$

So distance between $(1,2)$ and $P(x,y)$ is $\sqrt{{(x-1)}^2+{(y-2)}^2}$

and distance between $(-2,3)$ and $P(x,y)$ is $\sqrt{{(x-(-2))}^2+{(y-3)}^2}$

So, $\sqrt{{(x-1)}^2+{(y-2)}^2}=\sqrt{{(x-(-2))}^2+{(y-3)}^2}$

Squaring , we get

$x^2+y^2-2x-4y+5=x^2+y^2+4x-6y+13$

$⟹6x-2y+8=0$

Locus of point of equal distance from both the points is a straight line.