The equation of a circle whose center is at the origin and whose circumference is divided into 1:2 parts by a straight line 3x + 4Y + 15 = 0 is______ ．

As shown in the figure, because the circle is divided into two parts by the straight line 3x + 4Y + 15 = 0, so ∠ AOB = 120 ° and the distance from the center of the circle to the straight line 3x + 4Y + 15 = 0, d = 1532 + 42 = 3, in △ AOB, OA = 6 can be obtained. So the equation of the circle is x2 + y2 = 36. So the answer is: x2 + y2 = 36

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