Coordinate Geometry Question 130
Question: If the distance of any point P from the point $ A(a+b,a-b) $ and $ B(a-b,a+b) $ are equal, then the locus of P is
[Karnataka CET 2003]
Options:
A) $ x-y=0 $
B) $ ax+by=0 $
C) $ bx-ay=0 $
D) $ x+y=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
Let coordinate of point P is (x, y) Given $ PA=PB\Rightarrow {{(PA)}^{2}}={{(PB)}^{2}} $
$ \Rightarrow {{{x-(a+b)}}^{2}}+{{{y-(a-b)}}^{2}} $
$ ={{{x-(a-b)}}^{2}}+{{{y-(a+b)}}^{2}} $
$ \Rightarrow 2x[-a-b+a-b]+2y[-a+b+a+b]=0 $
$ \Rightarrow x(-2b)+y(2b)=0 $
$ \Rightarrow -x+y=0\Rightarrow x-y=0 $ .
BETA
