Chapter 11.2, Problem 45SPR

To determine

To find:

The equation of the fourth ring.

Answer to Problem 45SPR

The equation of the fourth ring is $x^2+y^2={\left(r+40\right)}^2$ .

Explanation of Solution

Given information:

Meteorologists track severe storms using Doppler radar. A polar grid is used to measures distances as the storms progress. If the center of the radar screen is the origin and each ring is $10$ miles farther from the center.

Calculation:

The equation of circle is:

  ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$

If the center of the radar screen is the origin and each ring is $10$ miles farther from the center.

  $\left(h,k\right)=\left(0,0\right)$

  $radius=\left(r+40\right)$

So, the equation of the fourth ring is:

  $x^2+y^2={\left(r+40\right)}^2$

Hence, the equation of the fourth ring is $x^2+y^2={\left(r+40\right)}^2$ .