Question

Help me pls

Square RSTU is inscribed in circle P. Given the coordinates for the vertices of the square, find the equation of circle P.
R(0, 4), S(6, 2), T(4, -4), and U(-2, -2)

Answer 1

9514 1404 393

Answer:

(x -2)² +y² = 20

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