Question

Find the locus of point P if PA=PB. Coordinates of. A(4,0)
and B(-4,0)

Answer 1

$\textbf{Given:}$

$\text{Given points are A(4,0) and B(-4,0) and PA=PB}$

$\textbf{To find:}$

$\text{The locus of P}$

$\textbf{Solution:}$

$\text{Let the coordinates of the moving point P be (h,k)}$

$\text{Condition:}$

$PA=PB$

$\sqrt{(h-4)^2+(k-0)^2}=\sqrt{(h+4)^2+(k-0)^2}$

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

$\text{Squaring on bothsides, we get}$

$(h-4)^2+k^2=(h+4)^2+k^2$

$(h-4)^2=(h+4)^2$

$h^2+16-8h=h^2+16+8h$

$-8h=8h$

$16h=0$

$\implies\,h=0$

$\therefore\textbf{The locus of P is x=0}$

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