Question

Hi find the equation of locus of point equidistant from the points (1,3) (5,7)​

Answer 1

$\textbf{Given:}$

$\textsf{Points are (1,3) and (5,7)}$

$\textbf{To find:}$

$\textsf{The locus of a point which is equidistant from the}$

$\textsf{given two points}$

$\textbf{Solution:}$

$\textsf{Let the given points be A(1,3) and B(5,7)}$

$\textsf{Let P(h,k) be the moving point}$

$\textsf{As per given data,}$

$\mathsf{PA=PB}$

$\mathsf{\sqrt{(h-1)^2+(k-3)^2}=\sqrt{(h-5)^2+(k-7)^2}}$

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

$\mathsf{(h-1)^2+(k-3)^2=(h-5)^2+(k-7)^2}$

$\mathsf{h^2+1-2h+k^2+9-6k=h^2+25-10h+k^2+49-14k}$

$\mathsf{10-2h-6k=74-10h-14k}$

$\mathsf{8h+8k-64=0}$

$\mathsf{h+k-8=0}$

$\therefore\mathsf{The\;locus\;of\;P\;is}$

$\boxed{\mathsf{x+y-8=0}}$

$\textbf{Find more:}$

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

and B(-4,0)

https://brainly.in/question/18378699

The locus of the point which is equidistant from the points (-2,2) and (3,0) is

https://brainly.in/question/34702598