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.

• A. $x - y = 0$
• B. $ax + by = 0$
• C. $bx - ay = 0$
• D. $x + y = 0$

Answer 1

Answer: (A)

$x - y = 0$

Answer 2

Let coordinate of point P is (x, y)

Given $P A = P B \Rightarrow ( P A ) ^ { 2 } = ( P B ) ^ { 2 }$

$\Rightarrow \{ x - ( a + b ) \} ^ { 2 } + \{ y - ( a - b ) \} ^ { 2 }$

$= \{ x - ( a - b ) \} ^ { 2 } + \{ y - ( a + b ) \} ^ { 2 }$

$\Rightarrow 2 x [ - a - b + a - b ] + 2 y [ - a + b + a + b ] = 0$

$\Rightarrow x ( - 2 b ) + y ( 2 b ) = 0$ $\Rightarrow - x + y = 0 \Rightarrow x - y = 0$.