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

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Let point $P(x, y)$ which is equidistant from the points $(2,3)$ and $(4,5)$. $ \begin{array}{cc} 	herefore & (x-2)^2+(y-3)^2=(x-4)^2+(y-5)^2 \ \Rightarrow & x^2-4 x+4+y^2-6 y+9 \ \Rightarrow & =x^2-8 x+16+y^2-10 y+25 \ \Rightarrow & 4 x+4 y=41-13 \ \Rightarrow & 4(x+y)=28 \ \Rightarrow & x+y=7 \end{array} $

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

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