Q:

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.

Accepted Solution

A:
Answer:[tex](x-15)^2+(y-30)^2=36[/tex]Step-by-step explanation:we know thatThe 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 unitsthereforeIf the radius of the circular flower garden in the actual is 60 feetthen the radius of the circular flower garden in the blueprint is 6 unitsFind the center of the radius in the blueprintRemember that the circular flower garden is in the center o the backyardsoTo find out the center, determine the midpoint of the rectangular backyardC((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 centerr is the radiuswe 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]