Question

A sprinkler set in the middle of a lawn sprays in a circlular pattern the area of the lawn that gets sprayed by the sprinkler can be described by the equation (x-2)y+(y-5)2=169

Answer 1

The equation (x-2)y+(y-5)²=169 describes the circular pattern of a sprinkler set in the middle of a lawn.

To see why, we can rewrite the equation in standard form for a circle:

(x-2)y+(y-5)²=169

xy - 2y + y² - 10y + 25 = 169

x(y-2) + y² - 10y - 144 = 0

(x-(-2))(y-5)² = 144

(x+2)(y-5)² = 144

This is the equation of a circle with center (-2, 5) and radius 12. Therefore, the area of the lawn that gets sprayed by the sprinkler is a circle with center (-2, 5) and radius 12.