The centre of the circle concentric with the circle x2 + y2 - 2x + 4y - 1 = 0 is:
Correct answer: C. (1, - 2)
- A. (2, -1)
- B. (-1, 2)
- C. (1, - 2)
- D. (-1, -2)
Explanation
To find the center of the circle given by the equation x2 + y2 - 2x + 4y - 1 = 0, we compare it with the standard form (x - h)2 + (y - k)2 = r2. The coefficients of x and y are -2 and 4, respectively. This means:The x-term is -2x, which gives us -2g = -2, hence g = 1.The y-term is 4y, which gives us -2f = 4, hence f = -2.Thus, the center of the circle is (1, -2), which is option C. The other options do not satisfy these computations, as they either have incorrect signs or incorrect values derived from the coefficients.
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