Let's begin by recalling the standard equation of a circle. In this equation, ( h, k) represents the center of a circle and r is the radius.
(x- h)^2+(y- k)^2= r^2
In the exercise, it is a given that the sprinkler waters a circular area that has a diameter of 10 feet.
Using this information, we can find the radius of the circle. Recall that a diameter of a circle is two times the radius. That can be shown in the following expression.
10=2 r ⇒ r=5
With that solved, let's move on to the other given information. We know that the sprinkler is located 20 feet north of the house, which is located at the origin. This means that we need to add 20 to the y-coordinate of the location of the house.
To further demonstrate what just occurred, see the following expression.
(0,0+20) ⇒ (0,20)
Gathering what we now know, the radius of the circle is 5 and the center point is ( 0, 20). Let's substitute these values into the standard equation of a circle.
