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Answer:
(x -2)² +y² = 20
Step-by-step explanation:
The center of the circle is the midpoint of either diagonal of the square. The midpoint of RT is ...
(R +T)/2 = ((0, 4) +(4, -4))/2 = (4, 0)/2 = (2, 0)
The square of the radius is the square of the distance between the center any any point on the circle. The distance (squared) from the center to R is ...
d² = (x2 -x1)² +(y2 -y1)²
d² = (0 -2)² +(4 -0)² = 4 +16 = 20
The circle with radius² = r² and center (h, k) has equation ...
(x -h)² +(y -k)² = r²
Our circle has (h, k) = (2, 0) and r² = 20, so the equation is ...
(x -2)² +y² = 20
