Chapter 14.1, Problem 14PSB

To determine

To write an equation for the locus of points $6$ units from the point $(-1,3)$ .

Answer to Problem 14PSB

  ${(x+1)}^2+{(y-3)}^2=6^2$

Explanation of Solution

Given:

The given circles passing through two given points.

Calculation:

The locus is a circle with radius $4$ units and the equation of the circle is given by the following equation-

  ${(x-h)}^2+{(y-k)}^2=r^2$

Here $(h,k)=(-1,3)$

And $r=6$ units.

So, the equation of the circle will be −

  $\begin{array}{l}$ {(x+1)}^2+{(y-3)}^2=6^2$x^2+2x+1+y^2+9-6y=36\\ x^2+2x+y^2-6y+10=36\end{array}$