The equation of the locus of points which are equidistant from the points $(2,3)$ and $(4,5)$ is

The equation of the locus of points which are equidistant from the points $(2,3)$ and $(4,5)$ is
  1. $x+y=0$
  2. $x+y=7$
  3. $4 x+4 y=38$
  4. $x+y=1$

Solution

$\begin{aligned} & \text { Let } P(x, y) \text { be equidistance from } A(2,3) \text { and } B(4,5) \\ & \Rightarrow(P A)^2=(P B)^2 \\ & \Rightarrow(x-2)^2+(y-3)^2=(x-4)^2+(y-5)^2 \\ & \Rightarrow \\ & x^2-4 x+4+y^2+9-6 y=x^2+16-8 x+y^2+25-10 y \\ & \Rightarrow 4 x+4 y=28 \Rightarrow x+y=7\end{aligned}$

Asked in: AP EAMCET 2024 (22 May Shift 1)

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