Fencing encloses a rectangular backyard that measures 300 feet by 600 feet. A blueprint of the backyard is drawn on the coordinate plane so that the rectangle has vertices (0,0),(0,60),(30,60) , and (30,0) .

A circular flower garden is dug to be exactly in the center of the backyard, with a radius of 60 feet. This garden is represented on the blueprint.

What is the equation of the flower garden represented on the blueprint? Enter your answer by filling in the boxes.

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calculista calculista · Answer 1 · 2019-11-27T10:53:30+01:00

Answer:

[tex](x-15)^2+(y-30)^2=36[/tex]

Step-by-step explanation:

we know that

The dimensions of the rectangular backyard in the actual are 300 feet by 600 feet

The dimensions of the rectangular backyard in the blueprint are 30 units by 60 units

therefore

If the radius of the circular flower garden in the actual is 60 feet

then

the radius of the circular flower garden in the blueprint is 6 units

Find the center of the radius in the blueprint

Remember that the circular flower garden is in the center o the backyard

so

To find out the center, determine the midpoint of the rectangular backyard

C((0+30)/2,(0+60)/2)

C(15,30)

The equation of a circle in center radius form is equal to

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where

(h,k) is the center

r is the radius

we have

[tex](h,k)=(15,30)\\r=6\ units[/tex]

substitute

[tex](x-15)^2+(y-30)^2=6^2[/tex]

[tex](x-15)^2+(y-30)^2=36[/tex]