Class 10

Math

All topics

Coordinate Geometry

If the distance of $P(x,y)$ from $A(5,1)$ and $B(−1,5)$ are equal then pove that $3x=2y$.

Point $P(x,y)$ is equidistant from the points $A(5,1)$ and $B(−1,5)$, means $PA=PB$ or $PA_{2}=PB_{2}$

$(5−x)_{2}+(1−y)_{2}=(−1−x)_{2}+(5−y)_{2}$

$(25+x_{2}−10x)+(1−y_{2}−2y)=(1+x_{2}+2x+25+y_{2}−10y)$

$26+x_{2}−10x+y_{2}−2y=(26+x_{2}+2x+y_{2}−10y)$

$12x=8y$

$3x=2y$

Hence proved.