Given the circle x2 + Y2 + KX + 2Y = - K2, when the area of the circle is the largest, the coordinate of the center of the circle is______ ．

Given the circle x2 + Y2 + KX + 2Y = - K2, when the area of the circle is the largest, the coordinate of the center of the circle is______ ．

Circle x2 + Y2 + KX + 2Y = - K2, the standard equation is (x + K2) 2 + (y + 1) 2 = − 34k2 + 1, when the area of the circle is the largest, the radius is the largest, ｜ k = 0 ｜ the equation of the circle is x2 + (y + 1) 2 = 1, the coordinates of the center of the circle are (0, - 1), so the answer is: (0, - 1)

Given that the line L: x-2y-5 = 0 and the circle C: x2 + y2 = 50, find: (1) the coordinates of intersection a and B; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; (2) the area of △ AOB

(1) The simultaneous equation x − 2Y − 5 = 0x2 + y2 = 50 can be obtained, Y2 + 4y-5 = 0 solution can be obtained, x = 7Y = 1 or x = − 5Y = − 5, that is, the intersection coordinates a (7,1) B (- 5, - 5) (2) let the intersection point m (5,0) s △ AOB = s △ AOM + s △ BOM = 12om · Ya + 12om · (− Yb) = 12 × 5 × (ya − Yb) = 52 × 6 = 15

Given that the line L: x-2y-5 = 0 and the circle C: x2 + y2 = 50, find: (1) the coordinates of intersection a and B; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; (2) the area of △ AOB

(1) The simultaneous equation x − 2Y − 5 = 0x2 + y2 = 50, Y2 + 4y-5 = 0, x = 7Y = 1 or x = − 5Y = − 5, i.e. the intersection coordinates a (7,1) B (- 5, - 5) (2) let the intersection point m (5,0) s △ AOB = s △ AOM + s △ BOM = 12om · Ya + 12om · (- Yb) = 12 × 5