Given the real number x, y satisfies the relation: x2 + y2-2x + 4y-20 = 0, then the minimum value of x2 + Y2 is 30-10530-105

Given the real number x, y satisfies the relation: x2 + y2-2x + 4y-20 = 0, then the minimum value of x2 + Y2 is 30-10530-105

The equation of a circle is transformed into a standard equation: (x-1) 2 + (y + 2) 2 = 25, then the a coordinate of the center of the circle is (1, - 2), and the radius of the circle is r = 5. Let the coordinates of a point on the circle be (x, y), and the o coordinate of the origin be (0, 0), then | Ao | = 5, | ab | = r = 5, so | Bo | = | ab | - | OA | = 5-5. Then the minimum value of x2 + Y2 is (5-5) 2 = 30-105