The equation of the locus of a point which is always equidistant from the points $(1,0)$ and $(0,-2)$ is :

• Correct answer
  A

  $2 x+4 y+3=0$
• B

  $4 x+2 y+3=0$
• C

  $2 x+4 y-3=0$
• D

  $4 x+2 y-3=0$

Solution

$\begin{aligned} & \mathrm{AC}^2=\mathrm{BC}^2 \\ & \Rightarrow(x-1)^2+(y-0)^2=(x-0)^2+(y+2)^2 \\ & \Rightarrow x^2-2 x+1+y^2=x^2+y^2+4 y+4 \\ & \quad-2 x-4 y-3=0 \Rightarrow 2 x+4 y+3=0\end{aligned}$

Hence, the correct answer is option: 'A'.