Area of a watered circle?

Question

A sprinkler waters a circular area that has a diameter of 10ft. The sprinkler is located 20ft north of the house. If the house is located at the origin what is the equation for the circle area that is watered?

Answer 1

the equation of a circle is given by the formula  (x-h)^2 + (y-k)^2 = r^2

where the center of the circle is at point (h,k) and r is the radius of the circle

 

In this instance the center of the circle is 20 ft north of the "origin" or at coordinates (0,20)

so (h,k) = (0,20)

 

The radius is half the diameter so r = 5 ft

 

Plugging into the formula you get the equation   (x-0)^2 + (y-20)^2 = 5^2

 

x^2 + (y-20)^2 = 25  is the equation of the circular area watered

 

This can be worked out further if necessary