Chapter 9.3, Problem 18PPS

To determine

To Find: The equation for the other limit of the detection area.

Answer to Problem 18PPS

  ${(x-5)}^2+{(y-10)}^2=400$

Explanation of Solution

Given: The radar for a country airport cannot control towers is located at $(5,10)$ on a map. It can detect up to $20$ miles away.

Given: $center:(5,10),r=20units$

The center of the circle is at $(h,k)$ and radius is at $r$

Equation of the circle

  ${(x-h)}^2+{(y-k)}^2=r^2$

Then

  $\begin{array}{}$ {(x-h)}^2+{(y-k)}^2=r^2$$ {(x-5)}^2+{(y-10)}^2={20}^2$$ {(x-5)}^2+{(y-10)}^2=400$\end{array}$

Hence, ${(x-5)}^2+{(y-10)}^2=400$