Question

Jenni plots her house and yard on a computer. she determines that the circle that defines the part of the front yard that gets watered by the sprinkler is (x−9)2 (y 11)2=16. what is the diameter, in meters, of the circular area that gets watered by the sprinkler? 4 m 8 m 16 m 32 m

Answer 1

The length of the diameter, in meters, of the circular area that gets watered by the sprinkler for this condition is given by: Option B: 8 m

What is the equation of the circle of radius r units, centered at (x,y) ?

If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as:

$(x-h)^2 + (y-k)^2 = r^2$

For this case, the equation of the circle that models tha circular area considered is:

$(x-9)^2 + (y+11)^2=16$

Writing this in standard form and comparing it with the standard equation, we get:

$(x-9)^2 + (y+11)^2=16\\(x-9)^2 + (y - (-11) )^2 = 4^2$ (didn't took (-4)² = 16 since radius cannot be negative).

Thus, we get center's coordinate as (9,-11) and radius of 4

The diameter of that circular area = twice of radius of the circle which models it = 2 × 4 = 8 meters.

Thus, the length of the diameter, in meters, of the circular area that gets watered by the sprinkler for this condition is given by: Option B: 8 m

Learn more about equation of a circle here:

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