Chapter 14.1, Problem 22PSB

To determine

To write an equation for the locus of points equidistant from $(3,5)$ and $(1,-9)$

Answer to Problem 22PSB

  $\sqrt{{\left(x-3\right)}^2+{(y-5)}^2}=\sqrt{{\left(x-1\right)}^2+{(y+9)}^2}$

Explanation of Solution

Given:

The points equidistant from $(3,5)$ and $(1,-9)$ .

Calculation:

Using the distance formula, the equation for the locus of points equidistant from $(3,5)$ and $(1,-9)$ can be found as follows-

The below is the equation

  $\begin{array}{l}\sqrt{{\left(x-3\right)}^2+{(y-5)}^2}\\ =\sqrt{{\left(x-1\right)}^2+{(y+9)}^2}\end{array}$