The general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.
According to the question,
The general form of the equation for the given circle centered at o(0, 0) is (x-h)² + (y-k)² = r².
- The given equation is x² + y² - 41 = 0 which is also represented by
(x-0)² + (y-0)² = -(√41)². This is not possible.
- The given equation is x² + y² - 41 = 0 which is also represented by (x-0)² + (y-0)² = (√41)²This means that the circle is centered at (0,0). Thus, the equation is correct
- The given equation is x² + y² +x+ y- 41 = 0 which is also represented by (x+1/2)² + (y+1/2)² = (√(83/2))²This means that the circle is centered at (-1/2,-1/2). Thus, this equation is incorrect.
- The given equation is x² + y² +x- y- 41 = 0 which is also represented by (x+1/2)² + (y-1/2)² = (√(83/2))²This means that the circle is centered at (1/2,-1/2). Thus, this equation is incorrect.
Hence, the general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.
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