The equation of a circle is given by \(x^{2} + y^{2} - 4x - 2y - 3\). Find the radius and the coordinates of its centre.
A. \(3, (-1, 2)\) B. \(2\sqrt{2}, (2, -1)\) C. \(2\sqrt{2}, (2, 1)\) D. \(9, (2, 1)\) Correct Answer: CExplanationEquation of a circle with radius r and centre (a, b). = \((x - a)^{2} + (y - b)^{2} = r^{2}\) Expanding, we have \(x^{2} - 2ax + a^{2} + y^{2} - 2by + b^{2} = r^{2}\) Comparing, with \(x^{2} + y^{2} - 4x - 2y - 3 = 0\) \(2a = 4 \implies a = 2\) \(2b = 2 \implies b = 1\) \(r^{2} - a^{2} - b^{2} = 3 \implies r^{2} = 3 + 2^{2} + 1^{2} = 8\) \(r = 2\sqrt{2}\) |