Question

Locus of a point which is equidistant from the point $(3,4)$ and $(5,-2)$ is a straight line whose $x-$intercept is

• A. $1/3$
• B. $2/3$
• C. $1$
• D. $-1/3$

Answer 1

Answer: (C)

$1$

$\text{Given}$

$\text{Locus of point which is equidistant from}$

$\text{the point}(3,4)\text{and}(5,-2)\text{is a straight line}$

$\text{whose}x\text{- intercept is}X$

$\text{Let table point}(h,k)$

$\text{So, distance from}(3,4)\text{and}(5,-2)\text{is equal}$

$\sqrt{(h-3{)}^2+(k-4{)}^2}=\sqrt{(h-5{)}^2+(k+2{)}^2}$

$h^2+9-6h+k^2+16-8k=h^2+25-10h+k^2+4+4k$

$9-6h+16-8k=-10h+25+4+4k$

$4h-12k+25-29=0$

$4h-12k=4$

$h-3k=1$

$x-$ intercept, $X=1$

option $C$ is correct.