Question

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

• A. $x+y=0$
• B. $x+y=7$
• C. $4x+4y=38$
• D. $x+y=1$

Answer 1

The correct option is B $x+y=7$

Locus point $=(x,y)$

$\sqrt{(x-2{)}^2+(y-3{)}^2}=\sqrt{(y-5{)}^2+(x-4{)}^2}$

$\Rightarrow (x-2{)}^2+(y-3{)}^2=(x-4{)}^2+(y-5{)}^2$

$\Rightarrow x^2+4-4x+y^2+9-6y=x^2+16-8x+y^2+25-10y$

$\Rightarrow 13-4x-6y=41-8x-10y$

$\Rightarrow -4x+8x-6y+10y=41-13$

$\Rightarrow 4x+4y=28$

$\Rightarrow x+y=7$.