It is known that the equation of the line where the edge CD of square ABCD is located is x-3y-4 = 0, the intersection point of diagonal AC and BD is p (5.2) It is known that the equation of the line where the edge CD of square ABCD is located is x-3y-4 = 0, the intersection point of diagonal AC and BD is p (5.2) Solving the equation of the line where AB edge is located The equation for finding the circumcircle of square ABCD

(1) Because CD: x-3y-4 = 0ab / / CD, let AB: x-3y + M = 0, (m ≠ - 4) ∵ diagonal AC, the intersection point of BD is p (5.2) ∵ p to AB, which is equal to the distance between P and CD | 5-3 * 2 + m | / √ 10 = | 5-3 * 2-4 | / √ 10 | M-1 | = 5, M-1 = ± 5, the solution of M = 6, or M = - 4 (rounding off) ∵ AB equation is x-3y + 6 = 0 (2) ∵

The two diagonals of rectangle ABCD intersect at point m (1,0), the equation of the line where AB side is located is x-3y-6 = 0, and the point t (- 1,1) is on the line where ad side is located
(1) Solving the equation of the line where ad edge is located
(2) The equation of solving rectangular ABCD circumcircle
(3) If the moving circle P passes through point n (- 1,0) and is circumscribed with the circumscribed circle of rectangle ABCD, the trajectory equation of the center of the moving circle P is obtained

(1) Ad, AB, so kad = - 1 / KAB = - 3,
So the ad equation is Y-1 = - 3 * (x + 1), and it is reduced to 3x + y + 2 = 0
(2) The circumscribed circle of rectangle ABCD takes m as the center and Ma as the radius,
Because m (1,0), x-3y-6 = 0 and 3x + y + 2 = 0, a (0, - 2) is obtained,
So R ^ 2 = | Ma | ^ 2 = (1-0) ^ 2 + (0 + 2) ^ 2 = 5,
Therefore, the equation of circumcircle of rectangle ABCD is (x-1) ^ 2 + y ^ 2 = 5
(3) (this is a mistake. N is in a circle, and a circle passing through n cannot be circumscribed.)

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